25,270 Answered Questions for the topic calculus

Calculus Precalculus

09/27/23

Sketch the graph of the following function and determine its domain and range.
1. f(x)= x² - 81/ x+92. f(x)=√9-x²3. f(x) = {x² -1 if x<3 at x= 3 {x+5 3≥x
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Calculus Precalculus

09/27/23

10.lim h-->0 (x+h)²-x²/ h h-->0
1. lim (x+h)²-x²/ h h-->0
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Calculus Precalculus

09/27/23

Find the derivative of the following using the definition of derivative. Write the solution of this answer. Use Limits of Delta X approaching zero
3. y = √xAnswer: 1/2√x4. f(x) = 1/3xAnswer: -1/3x²
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Calculus

09/27/23

II. Let ƒ and g be functions defined by f(x)=√x+2; g(x) = x²-4. Find the following:
1. f ∘ g2. g ∘ f
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Calculus

09/27/23

Derivatives as a function

Find the derivative of f(x)= 8/x2 using the limit definition of the derivative.
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Calculus

09/26/23

Find the derivative of the functions

Find the derivative of the functions f(x)=x^2+2x-1 and g(x)=1/2x^3-4x+1.
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Calculus

09/26/23

I need help with this problem!
Find the linear equation of the plane through the point (1,2,3) and contain the line represented by the vector equation r(t)= <3t, 5-4t, 1-8t)My answer was: 16x+14y+5z=59, but it is wrong. I... more
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Calculus

09/26/23

Can someone prove this why my answer is wrong?
Find the linear equation of the plane through the point (1,2,3) and contains the line represented by the vector equation r(t)= <3t, 5-4t, 1-8t)My answer was: 16x+14y+5z=59 but it is wrong. I... more
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Calculus

09/26/23

Tangent and revenue world problem help
1.) write the tangent line to graph of y=(6x^2-6x+3)(1+2x)2.) suppose the revenue in dollars from the sale of X units of a product is given by r(x)= 40x^2+45x/2x+2. Find the marginal rev when 45... more
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Calculus

09/26/23

Find the largest area of the largest rectangle that can be cut from a circular quadrant.
A rectangle with sides parallel to the coordinate axes is inscribed inthe ellipse.x^2/a^2+y^2/b^2=1Find the largest possible area for this rectangle.been stuck on this problem for a while and can't... more
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Calculus

09/26/23

Can someone help me solve this problem
Find the distance between the skew lines P(t)= <1,4,-4>+ t<-3,-3,-2> and Q(t)=(5,-1,-3)+ t<0,-2,-1>Given Hint: Take the cross product of the slope vectors of P and Q to find a... more
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09/26/23

Helpp!! Urgent Mid term practice, i need verification. ASAP
PLEASE HELP OUT!! I really need to confirm my answers. I would really appreciate it1) Solve. Answer in interval notation, restricting your attention to −𝜋 ≤ x ≤ 𝜋.sin2(x) < 1/2I got (0, 𝜋/2) U... more
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Calculus Math

09/25/23

Horizontal tangent problem
Find a cubic polynomial that has horizontal tangents at the points (-3,5) and (3,-2).
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Calculus Math

09/25/23

Tangent line problem

For what values of x in [x,2pi] does the graph of r(x)=x+2sinx have a horizontal tangent?
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Calculus Math

09/25/23

Finding all values that equal 0
Let q(x)=x^3+3x^2-144x+18Find all values of x at which q'(x)=0
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Calculus Math

09/25/23

Finding tangent line problem
Find an equation of the line tangent to the curve y=6^x at point (2,36)
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Calculus Math

09/25/23

Finding tangent line
Find an equation of the line tangent to the graph of y= 3/x^2 at the point (4/3/16)
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Calculus Math

09/25/23

Derivative rule problem

Given a power function of the form u(s)=as^n with u'(2)=20 and u'(6)=540, find n and a.
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Calculus

09/25/23

At noon, ship A is 180 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
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Calculus

09/25/23

At noon, ship A is 180 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
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Calculus

09/25/23

Piecewise Function
Using the piecewise function P(x)={3x-45, 0 ≤ x ≤ 50}, {3x-65, 50 < x ≤ 100}, {3x-85, 100 < x ≤ 150}Find P(10) and P(50) and explain why they satisfy the first part of the function which is... more
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Calculus

09/25/23

Depreciation Problem
In 2020, a manufacturing company purchased a new fabricating machine for $317,000. For tax purposes, the machine depreciates at a constant rate for 20 years, after which its book value is $0.a. ... more
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Calculus

09/25/23

I need help with this question! (Vector Funtion problem)
Find the arclength of the curve  r(t)= <2t^2, 2sqrt2, lnt>, for 1<= t <=4
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Calculus

09/25/23

What is the answer when theta is 70
A patrol car is parked 55 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 22 revolutions per minute. How fast is the light beam moving (in ft/sec)... more
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Calculus

09/25/23

Demand Functions

A developer of luxury tiny homes found that when they price a particular model of home at $95,000, they sell 70 homes each month and when they price the same model at $125,000, they sell 50 homes... more
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