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Calculus

02/02/24

Find the following limits. Try to use L'Hospital if possible.

a) lim as x approaches infinity of (2x+1)/(3x+1)I got type infinity/infinity so I started by finding f'(x)/g'(x) and writing ax as exlna. But I don't think this was correct.b) lim as x approaches 0... more

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Calculus

02/02/24

Use integration by parts to evaluate the following integrals.

∫x2lnxdxFor this one, do I set u=x^2 and dv=lnxdx? And so then would I use integration by parts to find v? Or would I set u=lnx and dv=x^2dx?

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Calculus

02/02/24

compute the derivatives of the following functions

Using the limit definition of derivativesf’(x) = lim h→0 f(x + h) − f(x)/hcompute the derivatives of the following functionsa) f(x) = 3x − 5(b) g(x) = −x2 + 9x(c) h(x) = 2/x − 9

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Calculus

02/01/24

find the value of the constant c that makes the following function continuous on (−∞ ∞)

f(b) = cb + 3, bE(-INF, 4] = cb^2 - 3, bE(4, INF)

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Calculus

02/01/24

Calculus I Single variable

A pole of length L is carried horizontally around a corner where a 2-ft-wide hallway meets a 9-ft-wide hallway, as shown in theπ figure on the right. For 0<0<2, find the relationship between... more

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Calculus

02/01/24

Use the product rule to find f(x) and then evaluate at the following points:

Let f(x) = (4x3 +7x + 5)(4x-2 - 6x-3. Use the product rule to find f(x) and then evaluate at the following points:(A) f′(12) = (B) f′(−12) =

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Calculus

02/01/24

Let y= f(x) = 3 - x^4 Find the increment in y, △y, when x changes from 0.4 to 1.3.

Let y= f(x) = 3 - x4 Find the increment in y, △y, when x changes from 0.4 to 1.3.

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Calculus

02/01/24

Find the instantaneous velocity of the particle after 3 seconds.

A particle moves along a coordinate line and s, its directed distance in centimeters from the origin after t seconds, is given by s = f(t) = √6t+7. Find the instantaneous velocity of the particle... more

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Calculus

02/01/24

How long will it take the falling object, initially at rest, falling due to gravity, to reach an instantaneous velocity of 96 feet per second?

How long will it take the falling object, initially at rest, falling due to gravity, to reach an instantaneous velocity of 96 feet per second?____ seconds.

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Calculus

02/01/24

Calculus Integrals involving Partial Fraction Decomposition and U Substitution

Evaluate the following integral by first applying the substitution rule with u=e^x followed by a partial fraction decomposition: ∫(5e^x+2)/(e^x+1)dx.

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Calculus Math

02/01/24

Evaluate the Integral using the given theorem.

Evaluate the Integral Below using the given theorem. DO NOT USE THE ANTIDERIVATIVE METHOD I need to learn how to use the definite integral method. Only use the theorem provided please. Please show... more

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Calculus Math

02/01/24

Evaluate the Integral Below:

Evaluate the Integral below using the theorem given. please show all steps. The correct answer is 39/2.

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Calculus Math

01/31/24

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. x = 8y^2 − 2y^3, x = 0

V = ???

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Answers •1

Calculus

01/31/24

Express the following functions in the form F = f ◦ g

F(x)=(√x+1)/√x

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Calculus

01/31/24

Compute the derivatives of the following functions.

Compute the derivatives of the following functions. You may use any derivative rules.(a) f(x) = x2 − 2x.(b) g(x) = 3x(x3 − 1).(c) h(t) = (3t2 − 9 / 2t3 + 5t) + 3/t

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Calculus

01/31/24

Find an equation for the tangent line to the graph

Find an equation for the tangent line to the graph of y = 3x2 − 7 at x = −1.

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Calculus Math

01/31/24

Evaluate the Integral Below:

Evaluate the Integral. please show all steps.

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Calculus Math

01/31/24

Use the form of the definition of the integral given to evaluate the integral. 1 to 5 of (3x^2 + 8x) dx

Use the form of the definition of the integral given, to evaluate the integral. 1 to 5 of (3x^2 + 8x) dx

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Calculus Math

01/30/24

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

A). √(1+x) on [-3,3]B). 3√(1-x) on [0,3]C). √(1+x) on [0,3]D). 3√(1+x) on [-3,3]E). 3√(1+x) on [0,3]Please show the whole process step by step.

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Calculus Math

01/30/24

Express the limit as a definite integral.

please show the whole process step by step so i can understand the problem.

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Calculus

01/30/24

Evaluate the integral

∫(from 0 to √(3)/4) dx/(1+16x2)

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Answers •3

Calculus Math

01/30/24

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 1 of (x^3 − 4x^2) dx

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Calculus Math

01/30/24

Use the form of the definition of the integral given in this theorem to evaluate the integral. 1 to 5 of (3x^2 + 8x) dx

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Answers •1

Calculus Math

01/30/24

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 4 of (9 − x^2) dx

Use the form of the definition of the integral given in the theorem to evaluate the integral. Integral 0 to 4 of (9 - x^2) dx

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Answers •1

Calculus

01/30/24

Find the derivative and evaluate the integral.

y=tan-1(x2)For this, I would utilize the derivative of arctan and chain rule, right? So with this, I'd get 1/(1+(x2)2)*(2x)? And by simplification, the answer would be (2x)/(1+(x2)2)?∫(from 0 to... more

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Find the following limits. Try to use L'Hospital if possible.

Use integration by parts to evaluate the following integrals.

compute the derivatives of the following functions

find the value of the constant c that makes the following function continuous on (−∞ ∞)

Calculus I Single variable

Use the product rule to find f(x) and then evaluate at the following points:

Let y= f(x) = 3 - x^4 Find the increment in y, △y, when x changes from 0.4 to 1.3.

Find the instantaneous velocity of the particle after 3 seconds.

How long will it take the falling object, initially at rest, falling due to gravity, to reach an instantaneous velocity of 96 feet per second?

Calculus Integrals involving Partial Fraction Decomposition and U Substitution

Evaluate the Integral using the given theorem.

Evaluate the Integral Below:

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. x = 8y^2 − 2y^3, x = 0

Express the following functions in the form F = f ◦ g

Compute the derivatives of the following functions.

Find an equation for the tangent line to the graph

Evaluate the Integral Below:

Use the form of the definition of the integral given to evaluate the integral. 1 to 5 of (3x^2 + 8x) dx

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

Express the limit as a definite integral.

Evaluate the integral

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 1 of (x^3 − 4x^2) dx

Use the form of the definition of the integral given in this theorem to evaluate the integral. 1 to 5 of (3x^2 + 8x) dx

Use the form of the definition of the integral given in this theorem to evaluate the integral. 0 to 4 of (9 − x^2) dx

Find the derivative and evaluate the integral.

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