25,270 Answered Questions for the topic calculus

Calculus Math

04/05/24

math question please help

A hot coffee just brewed(180F) from the coffee machine is placed in a room where the temperature is 65F. After 20 minutes, the hot coffee has cooled to 140F. Find the temperature after one hour 06... more
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Calculus

04/05/24

Find the equation of the tangent line to the graph of f (x) = x3 + 4х - 1) (x - 2) at the given point, (1, -4) . Write your answer in slope-intercept form, y = mx + b.
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Calculus

04/05/24

Find the linearization of the function f(x,y) = xsqrt(y) at the point (9,4).
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Calculus

04/05/24

Find the equation of the tangent plane to the surface e^(-4x/17)ln(3y) at the point (3, 4, 1.22673).
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Calculus

04/05/24

Sketching Graphs with derivatives
Sketch the graph of a function with the given characteristics:f(2)=f(4)=0f'(x)<0 for x<3f'(3) does not existf'(x)>0 for x>3 f''(x)<0, x≠ 3
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Calculus

04/04/24

Use the second fundamental theorem of calculus (and any integration techniques of your choice) to evaluate the following integrals.
Use the second fundamental theorem of calculus (and any integration techniques of your choice)to evaluate the following integrals.∫10 2x3 + x dx∫20 y2cos(y3 + 5) dy∫71 (t2 + 1)/(√2t3 + 6t) dt
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Calculus

04/04/24

Using the first fundamental theorem of calculus and the chain rule, find
Using the first fundamental theorem of calculus and the chain rule, findd/dx ∫x6 2sin(t2 + t + 5)dtd/dx ∫sin^3(x)5x 2sin(t2 + t + 5)dt
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Calculus

04/04/24

(a) When is the object moving backward and when is it moving forward? (b) Using (a), find the total distance travelled during the first 10 seconds.
An object is moving with velocity v(t) = 4t − 12 in feet per second.(a) When is the object moving backward and when is it moving forward?(b) Using (a), find the total distance travelled during the... more
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Calculus

04/04/24

Evaluate the two problems
Evaluate (a) ∫((2pi)/4)0 |sin(4x)|dx=______(b) ∫100pi0|sin(4x)|dx=______
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Calculus

04/04/24

an object at the origin at time t = 0 has velocity measured in meters per second,
an object at the origin at time t = 0 has velocity measured in meters per second, t/20 if 0 ≤ t ≤ 60v(t) = { 3 if 60 < t ≤ 120           9-t/20 if 120 <... more
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Calculus

04/04/24

Evaluate Integral of (10x^3+20x^2+20x-10)/((x+2)^2(x^2+6))dx
Show all steps please
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Calculus

04/04/24

Suppose the temperature in degress Fahrenheit of a metal bar of length 2 feet depends on the position x according the function
Suppose the temperature in degress Fahrenheit of a metal bar of length 2 feet depends on the position x according the functionT(x) = 40 + 20x(2-x^4)Find the average temperature in the bar _______Is... more
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Calculus

04/04/24

Evaluate Integral of (x^3+2x)/(sqrt(x^2-2))dx
Use u-sub or Trig substitution, I think
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Calculus

04/04/24

Find the average value of the function defined by f(x)on the interval[ 0,pi^(1/4)]
f(x) = x^3sin7x^4 on the interval [0,pi^(1/4)]
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Calculus

04/04/24

A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
(a) How much wire should be used for the square in order to maximize the total area?  m(b) How much wire should be used for the square in order to minimize the total area? m
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Calculus

04/04/24

A piece of wire 15 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (Give your answers correct to two decimal places.)
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04/04/24

Determine if W1 is a basis for R3 and check the correct answer(s) below
Here is the link to the question. A video would really help https://ibb.co/wc1mrxx
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Calculus

04/03/24

Help with optimization question

An oil refinery is located 1 km north of the north bank of a straight river that is 1 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the... more
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Calculus Python

04/03/24

(a) Find the critical values of the function.
4. Given{ f(x) = (10 −1/4x^2 ,if x < 0 {5e^(x−2)/2 − x ,if x ≥ 0.(a) Find the critical values of the function.(b) Find the absolute extrema of f on the interval [−5, 5].(c) Plot f on the... more
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Calculus

04/02/24

3.9 Related Rates
Suppose y = sqrt2x+1 where x and y are functions of t.(a)If dxdt = 9, find dydt when x = 4.dydt = 3 (b)If dydt = 4, find dxdt when x = 24.dxdt =
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Calculus

04/02/24

3.9 Related Rates

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 11 cm and the width is 6 cm, how fast is the area of the rectangle... more
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Calculus

04/02/24

3.9 Related Rates
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 mm? (Round your answer to two decimal places.)   mm3/s
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Calculus

04/02/24

3.9 Related Rates
At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00... more
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Calculus

04/02/24

4.1 Max and Mins
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)h(t) = t3/4 − 9t1/4t = 
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Calculus

04/02/24

4.1 Max and Mins

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)f(x) = x3e−8xx = 
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