Question 1
Find the derivative of f(x) = -10x2 + 4x at x = 11.
-216
-196
-176
-363

Question 2
Find the limit of the function by using direct substitution.
limit as x approaches four of quantity x squared plus three x minus one
Does not exist
-27
0
27

Question 3
Find the derivative of f(x) = 7x + 9 at x = 6.
7
9
6
0

Question 4
Find the indicated limit, if it exists.
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0
3
10
7
The limit does not exist.

Question 5
Find the derivative of f(x) = 3 divided by x at x = 1.
-3
-1
1
3

Question 6
Use the given graph to determine the limit, if it exists.
A coordinate graph is shown with a horizontal line crossing the y axis at four that ends at the open point 2, 4, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3.
Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..
-3; 4
1; 1
4; -3
Does not exist; does not exist

Question 7
Find the indicated limit, if it exists.
limit of f of x as x approaches negative 1 where f of x equals x plus 1 when x is less than negative 1 and f of x equals 1 minus x when x is greater than or equal to negative 1
-1
2
The limit does not exist.
0

Question 8
Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 7 as x approaches 7 from the left.
-∞ ; x = 7
∞ ; x = -7
-∞ ; x = -7
1 ; no vertical asymptotes

Question 9
Use the given graph to determine the limit, if it exists.
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1.5, a closed point at 3, 7, and a horizontal line starting at the open point 3, 2.
Find limit as x approaches three from the left of f of x..
7
1.5
Does not exist
2

Question 10
Find the limit of the function algebraically.
limit as x approaches zero of quantity x cubed plus one divided by x to the fifth power.
0
-9
Does not exist
9

Question 11
Find the derivative of f(x) = negative 3 divided by x at x = -4.
3 divided by 4
3 divided by 16
16 divided by 3
4 divided by 3

Question 12
Find the limit of the function by using direct substitution.
limit as x approaches zero of quantity x squared minus two.
2
-2
Does not exist
0

Question 13
Find the limit of the function algebraically.
limit as x approaches four of quantity x squared minus sixteen divided by quantity x minus four.
Does not exist
4
1
8

Question 14
The position of an object at time t is given by s(t) = -1 - 13t. Find the instantaneous velocity at t = 8 by finding the derivative.

Question 15

 Use graphs and tables to find the limit and identify any vertical asymptotes of the function. limit of 1 divided by the quantity x minus 2 squared as x approaches 2
in Other Math Topics by Level 1 User (200 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

2 Answers

Q1. f'(x)=-20x+4. When x=11, this is f'(11)=-20×11+4=-220+4=-216.

Q2. Lim(x➝4) of x²+3x-1. The expression can be evaluated by direct substitution without constraints: 16+12-1=27.

Q3. The derivative is 7 for all values of x because the function is linear with a constant slope.

Q4. The function is piecewise. We need the conditions that apply when x is close to zero. We need to look at x approaching from the negative side and the positive side. If the limits are not the same the limit does not exist. So, when x<0 we use 7-x². When x is just less than zero, this left-hand limit is 7. When x>0 we use 10x+7. When x is just bigger than zero, this right-hand limit is 7. We are not interested in x=0, we are only interested in the left- and right-hand limits, which happen to be the same. So the limit is 7.

Q5. f'(x)=-3/x². f'(1)=-3.

Q6.  In all limit questions, you can always ignore what happens when x=limit, because it’s the approaches that matter. So x➝2⁻ means look at the graph on the left of the limit. The horizontal line at y=4 means the left limit is 4. x➝2⁺ means look at the graph on the right of the limit. This is where y=-3, so the right limit is -3. The answer is 4 and -3 for left and right limits respectively.

Q7. First find left and right limits: x➝-1⁻: use x<-1: f(x)=x+1, so left limit is 0; x➝-1⁺: use x>-1: f(x)=1-x: so right limit is 1-(-1)=2. The left and right limits are different, so the limit does not exist.

Q8. 1/(x-7). When x=7, this quantity is not defined and this is a vertical asymptote. When x➝7⁻ we can use a value of x slightly less than 7 and see what happens. First try x=6.99, then 1/(x-7)=-100. Now try x=6.999, then we get -1000. So it’s getting larger in magnitude, and it’s negative. An infinitely large negative value is -∞. So the limit as x approaches 7 from the left is -∞.

Q9. Ignore the closed point at (3,7). For x➝3⁻, we are on the sloping line, so the limit is 1.5.

Q10. As x approaches zero the numerator approaches 1. The denominator gets smaller so its reciprocal gets larger, and it can be positive or negative depending on how we approach zero. So we can’t define the limit, so it doesn’t exist.

Q11. Derivative is -(-3/x²)=3/x². When x=-4, this is 3/16, because (-4)²=16.

Q12. x²-2➝-2 when x➝0.

Q13. (x²-16)/(x-4)=(x-4)(x+4)/(x-4)➝x+4 because the common factor x-4 cancels. Note that the quantity does not exist at precisely x=4 but in the limit it approaches x+4=8 when x=4. So the answer is 8 for the limit.

Q14. The derivative is constant -13 and is independent of t, so the instantaneous velocity is -13.

Q15. 1/(x-2)² is always positive, so it doesn’t matter whether we look at the left or right limits. The result as x➝2 is ∞, which is an undefinable quantity. x=2 is a vertical asymptote.

by Top Rated User (1.1m points)
panic of 1837
by

Related questions

1 answer
asked May 3, 2018 in Other Math Topics by Reema Level 1 User (200 points) | 520 views
2 answers
1 answer
asked May 2, 2018 in Other Math Topics by Reema Level 1 User (200 points) | 188 views
0 answers
asked Sep 30, 2012 in Algebra 1 Answers by Nyanlin Htetnaing Level 1 User (180 points) | 382 views
1 answer
asked Nov 14, 2012 in Word Problem Answers by anonymous | 387 views
1 answer
0 answers
1 answer
asked Jul 10, 2013 in Geometry Answers by JR Level 1 User (820 points) | 329 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,939 users