25,270 Answered Questions for the topic calculus

Calculus

01/26/24

AP Calculus BC -- Improper Integrals
∫ of e1/2 dy from infinity to 0. ∫ of dx/x-1 from 3 to 0. Number 1 is apparently that way, not sure if there are no typos.
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Calculus

01/26/24

Compute the following limits
a) limx→1 1 / x − 1=(b) lim x→1+ x + 2 / x − 1=(c) lim x→∞ 2x / x − 5 =(d) lim x→−∞ 5x2 − 6x3 / 7x4 + 2x − 9 —=
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Calculus

01/26/24

Consider the function

Consider the functionh(x) = −8x2/ 3x2 + 5x − 6(a) Find all the points where h(x) is discontinuous.(b) Find all horizontal asymptotes of h(x)
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Calculus

01/26/24

Use the fact that limx→0 sin(x)/x = 1 to compute the following limits.
(A.) lim x→0 sin(5x)/2x =(b.) lim t→0 sin2(3t)/t =(c) lim θ→0 sin(3θ)/tan(θ) =
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Calculus

01/25/24

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)
a= <2,2> b=<2,-1>exact=approximent=
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Calculus

01/24/24

Determine Increasing/Decreasing and Concavity
Given the function f(x)=x^3−48x^2, determine all intervals on which f is both increasing and concave up. I am also confused about when my teacher tested values and stated whether or not a number... more
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Calculus

01/24/24

Particle Motion from Equation
A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=t^5−5t^4. Determine all intervals when the acceleration of the particle is negative.
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Calculus

01/24/24

Related Rates (One Formula)
The radius of a cone is decreasing at a constant rate of 5 feet per second. The volume remains a constant 432 cubic feet. At the instant when the height of the cone is 66 feet, what is the rate of... more
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Calculus

01/24/24

Related Rates (Two Formulas)
The volume of a sphere is increasing at a constant rate of 198 cubic feet per second. At the instant when the volume of the sphere is 18 cubic feet, what is the rate of change of the surface area... more
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Calculus

01/23/24

Find a function that gives the number of bacteria present in the colony after t hours.

Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half an hour. (a) Find a function that gives the number of bacteria present in the colony after t hours. (b)... more
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Calculus

01/23/24

If v lies in the first quadrant and makes an angle 𝜋/3 with the positive x-axis and |v| = 4, find v in component form.
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Calculus

01/23/24

Suppose that a wind is blowing in the direction S45°E at a speed of 50 km/h. A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 100 km/h.
The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find... more
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Calculus

01/23/24

A woman walks due west on the deck of a ship at 3 mi/h.

A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 24 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your... more
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Calculus

01/23/24

A quarterback throws a football with an angle of elevation 40° and speed 80 ft/s. Find the horizontal and vertical components of the velocity vector. (Round your answers to one decimal place.)
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Calculus

01/23/24

Find a vector that has the same direction as −6, 4 but has length 6.
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Calculus

01/23/24

Find a unit vector that has the same direction as the given vector.

−5i + 9j
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Calculus

01/23/24

a + b, 2a + 3b, |a|, and |a − b|.
a = 2i + j,    b = i − 5j
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Calculus

01/23/24

Consider the function...
Please help. I cannot upload a photo, so I have tried to translate the limit of F(x,y) just using my keyboard.Question:Consider the function 𝑓(𝑥,𝑦)=(𝑥^𝑚)(𝑦^3)/((𝑥^2)+(𝑦^4)), where 𝑚∈𝐙 is a fixed... more
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Calculus

01/23/24

Evaluate the integral (natural log)
∫(1 to 2)e1/x/x2(dx)
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Calculus

01/23/24

Differentiate the natural logarithmic function
y=esin2x+sin(e2x)
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Calculus

01/23/24

Evaluate the limit of the natural logarithm:
the limit as x approaches infinity, e-2xcosx
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Calculus

01/23/24

Evaluate the integral of the natural logarithms.
∫(e to 6) of dx/(xlnx)I started off by separating dx so that it was (1/xlnx)dx and I used the ∫1/x(dx)=ln|x|+C identity so that the equation was ln|xlnx|+C but I'm not sure if that was correct or... more
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Calculus

01/23/24

When the cruiser is 0.5 km north of the intersection and the car is 0.8km to the east, the police determine with radar that the distance between them and the car is increasing 20km/h
A police cruiser, approaching a right- angled intersection from the north chasing a speeding car that hass turned the corner and now is moving straight east. When the cruiser is 0.5 km north of the... more
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Calculus

01/22/24

I have a quote to build 16 drawers plus remove 5 shelves for $3348.95. Now 8 drawers and 5 shelves.what should the quote be

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Calculus

01/22/24

Solve the initial value problem
Find the antiderivative that satisfies the conditionf(x) = 8x^3 - 2x^-2 ; F(1) = 5The answer is supposed to be 2x^4 + 2x^-1 + 1I am not sure what steps I need to take to get there.Solve the initial... more
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