25,270 Answered Questions for the topic calculus

Calculus

03/06/24

Using linear approximation and tangent
1.Let y=4x^2+2x+3. If Δx=0.3 at x=4, use linear approximation to estimate ΔyΔy≈2.Let y=sin(3x). If Δx=0.3 at x=0, use linear approximation to estimate ΔyΔy≈ =   Find the percentage errorerror... more
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Calculus

03/06/24

Word problems finding a lot of cm^3/mix&max as well as some other things :)
1.A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the radius is 9 cm. (Note the... more
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Calculus

03/06/24

Rotating Light in calculus
A rotating light is located 12 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's... more
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Calculus

03/06/24

Use implicit differentiation to find the slope of the tangent line to the curve
Use implicit differentiation to find the slope of the tangent line to the curvey/x-4y=x^3-5*y (numerator) x-4y (denominator)at the point (1,4/15).slope = 
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Calculus

03/06/24

Find the slope of the tangent line to the curve below at a point

Find the slope of the tangent line to the curve below at the point (7,5)sqrt x+y + sqrt2xy = 11.830701880479*sqrt is over both x+y*slope=
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Calculus

03/06/24

Finding dy/dx and the equation of the tangent line
Given the equation below, find dy/dx.-7x^7+3x^28 y+y^4=-3*Hint the x^28 are separate from the y so the y isn't included in the exponent.*dy/dx=Now, find the equation of the tangent line to the... more
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Calculus

03/06/24

Max velocity and max height!
A object is launched into the air vertically from ground level with initial velocity 250 m/s.What is the object's maximum velocity?    m/sWhat is the object's maximum height?    m
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Calculus

03/06/24

Find the derivative !!WITHOUT USING FRACTIONS AND NEGATIVE EXPONENTS!!
Find the derivative of f(x)= 6sqrt x-2/x^10.Type your answer without fractional or negative exponents. Use sqrt(x) for sqrtxf′(x)=
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Calculus Math

03/06/24

Evaluate the Trig integral. Show All Steps
Evaluate the Trig integral. Show All Steps. If possible can you attach a video going through it.
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Calculus

03/05/24

I have 2 questions for calculus homework, need the answers please, I am on my last attempt for submitting
Question 1: Find the high-order derivative. f"(x) = 4 √ x-6,Radical is over x-6^^^f^(5)(x) = ___________ Question 2: f(x) = (x + 2)(x − 2)(x + 7)(x − 7)f"(x) = 12x^2-106Solve the equation f''(x) =... more
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Calculus

03/05/24

Calculus - 2px + 5p = 300
1.The price p (in $) and demand x for a product are related by the equation 2px + 5p = 300. If the price is decreasing at a rate of $2 per month when the price is $10, find the rate of change of... more
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Calculus

03/05/24

Consider the following equation. 6x^2 − y^2 = 4
Find y' by implicit differentiation.Solve the equation explicitly for y and differentiate to get y' in terms of x.
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Calculus

03/05/24

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y^2(y2 − 4) = x^2(x^2 − 5). (0, −2) (devils curve)
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Calculus

03/05/24

urgent!! help please
integral 0 to sqrt 3 of x^3/sqrt (4-x^2) dx please show all steps to evaluate this integral
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Calculus

03/04/24

Compute the following limits. Clearly indicate the usage of L'Hospital's rule.
limit as x approaches ∞ [2ln(x)-ln(3x2+1)]
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Calculus

03/04/24

Evaluate the following integral
∫1/(4+t2)dt
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Calculus

03/04/24

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).]
e (raised to the exponent) 5 radical xg(x), f(u) = ?Find the derivate dy/dx = ?
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Calculus

03/04/24

Write the composite function in the form f(g(x)).  [Identify the inner function u = g(x)  and the outer function y = f(u).]
y = 3 (rad) 1 + 8x(g(x), f((u))= ? Find derivate = dy/dx
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Calculus

03/04/24

Suppose f(𝜋/3) = 2 and f '(𝜋/3) = −5, and let g(x) = f(x) sin(x) and h(x) = cos(x)/f(x). Find the following.
g'(𝜋/3)= h'(𝜋/3)= 
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Calculus

03/04/24

For what values of x does the graph of f have a horizontal tangent? (Use n as your integer variable. Enter your answers as a comma-separated list.) f(x) = x − 2 sin(x)
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Calculus

03/04/24

If f(x) = 6e^x cos(x), find f '(x) and f ''(x).
Find F'(x) and F''(x)
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03/04/24

I need help with this. Please

Assume this is a closed Leontief model.Consider an international trade model consisting of three countries X, Y, and Z. Suppose X uses 1/4 of its production domestically, sends 1/2 of its... more
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03/04/24

I need help with this, i think you are supposed to use matrices or something

Assume this is a closed Leontief model. We assume that in a village there are farmers, carpenters, and tailors, who provide the three essential goods: food, housing, and clothing. Suppose the... more
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Calculus

03/04/24

Volume of Ball in R⁴
How do you calculate the (four-dimensional) volume V = r⁴⋅π²/2 of the ball B(r) = {(x₁,x₂,x₃,x₄) ∈ R⁴: x₁²+x₂²+x₃²+x₄² ≤ r²}?
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Calculus

03/04/24

Given integral, find derivative. Help please!
If f(x) = ∫ [from 3 to x7+8x4+6] cos(t)dtthen f'(x) = ?Could someone please help me understand the steps required to solve this? Thanks so much!
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