25,270 Answered Questions for the topic calculus

Calculus Math

02/29/24

Evaluate the Integral (using Integration By Parts)
Evaluate the Integral (using Integration By Parts). Show a step by step solution. If possible could you make a video to go through the problem? the final answer is \frac{2\sqrt{3}\ln... more
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Calculus Precalculus

02/27/24

Pls help! Calculus
If f(x) = (e ^ x + e ^ (- x))/2 with domain confined to the interval [0, infinity), find the derivative of the inverse function by using the formula (f ^ - 1)' * (x) = 1/(f' * (f ^ - 1 * (x)))
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02/27/24

help out :) calculus
Use the implicit differentiation method to find the equation of the line that is tangent to the curve e ^ (- (x ^ 2 + y)) = x + y + 1 at the point P(1, 1).
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02/27/24

calculus help urgent
I have this question I got the answer but I think I am wrong cause idk what it means by [0, infinity). If f(x) = (e ^ x + e ^ (- x))/2 with domain confined to the interval [0, infinity), find the... more
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02/27/24

helpppp! calculus
If f(x) = (e ^ x + e ^ (- x))/2 with domain confined to the interval [0, 0), find the derivative of the inverse function by using the formula (f ^ - 1)' * (x) = 1/(f' * (f ^ - 1 * (x)))
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02/27/24

helpp!! :) Calculus
Find the equations of all lines that are tangent to the graph of the function f(x) = x ^ 2 + 1 and pass through the point P(1,0). Be careful: this point is not on the graph of f.
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Calculus

02/27/24

Estimate the rate of change of the temperature after an hour (in °F/min)
A roast turkey is taken from an oven when its temperature has reached 185°F and is placed on a table in a room where the temperature is 75°F. The graph shows how the temperature of the turkey... more
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Calculus

02/27/24

certain differentiable function f has a tangent line y = π2 x − π2 at the point on its graph where x = 1. If g is another function defined by g(x) = sin(3f(x)) + (f(x))2, what is g′(1
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Calculus

02/27/24

Determine whether the sequence converges or diverges. If it converges, find the limit. If necessary, use L'H rule.
an=n√(21+3n))In general, with roots and exponents, do you take the natural log in order to find the limit?
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Calculus

02/27/24

If f(t) is continuous for t≥0, the Laplace transform of f is the function F defined by this equation. Find the Laplace transforms of the following functions.
If f(t) is continuous for t≥0, the Laplace transform of f is the function F defined by:F(s)=∫(0 to ∞) f(t)e-stdtAnd the domain of F is the set consisting of all numbers s for which the integral... more
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Calculus

02/27/24

Evaluate the integral using methods of improper integrals
∫(0 to 4)dx/(x2-x-2)For this question, I would split the integral so that it would be ∫(0 to 1) dx/(x2-x-2)+ ∫(1 to 4) dx/(x2-x-2) right?So ∫(0 to 1)dx/(x2-x-2) = lim (t→1-) ∫(0 to t)... more
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Calculus

02/27/24

Evaluate the integral using the types of improper integrals.
∫(1 to ∞)([ln(x)]/x2)dxI started off by using the method of improper integrals: ∫(1 to ∞)([ln(x)]/x2)dx = lim (t→∞) ∫(1 to t)([ln(x)]/x2)dxI then used integration by parts with u=lnx and dv=1/x2dx,... more
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Calculus

02/27/24

AP Calculus BC - Mixing Problem
A 1400 gallon tank initially contains 600 gallons of water with 4 lbs of salt dissolved in it. Water with a salt concentration of 2 lbs/gallon enters the tank at a rate of 10 gal/h, while the... more
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Calculus

02/27/24

Write an equation for a function that has a graph with the given characteristics. The shape of y = 3 √ x shifted left 8 units and shifted up 3 units.
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Calculus

02/27/24

Solve for minutes and seconds
A Ferris wheel is 10 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel... more
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Calculus

02/26/24

Use the equation given below to find f '' ( 𝜋 /3) .
f(X)=sec(x)
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Calculus

02/26/24

Can you help me solve this (it's to know if the answer I have is correct), can it be step by step, please.
https://ibb.co/bWGc7kp
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Calculus

02/25/24

integration by partial fractions

integral ((6x^2+3x+6)/(x^3-1))
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Calculus

02/25/24

Find the Differentiate.

Y=x^4/1-x^3
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Calculus

02/25/24

Find the Differentiate
R(t)=(t+e^t)(8-√t)
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Calculus

02/25/24

Find the Differentiate
g(x) =5e^x√x
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Calculus

02/24/24

Find the average rate of change (in $ per unit) of C with respect to x when the production level is changed from x = 100 to the given value. (Round your answers to the nearest cent.)
The cost (in dollars) of producing x units of a certain commodity is C(x) = 8,000 + 12x + 0.15x2.(a)Find the average rate of change (in $ per unit) of C with respect to x when the production level... more
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Calculus

02/24/24

Matching Volume Integral Questions
Which of the following integrals represents the volume of the solid obtained by rotating the region bounded by the curves y = tan^3(x), y= 1, and x = 0 about the line y = 1?a) π ∫(tan^3(x))^2 dx... more
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Calculus

02/23/24

Find the 5th and 6th derivative
Find the 5th and 6th derivativey= x4 / 2 - 2/3 x2 -2x
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Calculus

02/23/24

If the radius of the tank is 20 feet and the water level fell at the rate of 4 feet per hour at 7 A.M., at what rate was water being used exactly at that time?
Webster City monitors the height of the water in its cylindrical water tank with an automatic recording device. Water is constantly pumped into the tank at the rate of 2300 cubic feet per hour. If... more
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