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Calculus

07/18/24

In exact fractional form

A boat starts off 34 miles directly west from the city of Uniontown. It travels due north at a speed of 41 miles per hour. After travelling 44 miles, how fast (in radians per hour) is the angle... more

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Calculus

07/18/24

Help me solve this

A boat starts off 34 miles directly west from the city of Uniontown. It travels due north at a speed of 41 miles per hour. After travelling 44 miles, how fast (in radians per hour) is the angle... more

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Calculus

07/14/24

Use the graph of f(x)=x2 below to find a number δ such that ∣∣x2−1∣∣<0.3 whenever 0<|x−1|<δ.

https://prnt.sc/4Ui0oj7qDSOX

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Calculus Algebra 2 Geometry

07/14/24

Find the critical points of the linear equation y = 4x^3 - 3x

So to be clear, when I state critical point, I want the maxima, minima, and any zeros in the domain of the function.

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Answers •4

Calculus Geometry

07/13/24

What is the angle between a position vector and a tangent?

If r=f(θ) is a differentiable curve and P(r0,θ0) is a point on that curve, derive the "formula" for the angle between the position vector and the tangent to f at P.

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Answers •1

Calculus

07/10/24

The ratio and root tests

Use the ratio tests to determine the ak of this series below.∞∑ (n𝜋^n)/(-4)^(n-1)n = 1 I know that it is convergent but I was not able to figure out the ak specifically.

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Calculus

07/10/24

Find the amount of oil that the field can be expected to yield during the first 6 years of production, assuming that the projection holds true

Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of R(t)=((600t^2)/(t^3+32))+5... more

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Calculus Geometry Trigonometry

07/09/24

Plane Curve with Constant Angle

Find a plane curve starting at (1,0) with a constant angle α = 75° between the tangent and position vector at each point.

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Calculus Math Algebra 2 Precalculus

07/05/24

Finding the stationary points of a given function

If given f(x) = x3ex,a) How can I find coordinates of the stationary point(s) of f(x)b) How can I determine the nature of the stationary point of f(x).c) On what interval is the function f(x)... more

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Calculus Math Precalculus

07/05/24

Proving u and v is perpendicular to the sum of 2u and v

Suppose u and v are such that the sum of u and v is perpendicular to u. If |v| =√(2)|u|, how can I prove that v is perpendicular to the sum of u and v .

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Calculus Math Algebra 2 Precalculus

07/05/24

Stationary points of a given function

If given f(x) = x3e3,a) How can I find coordinates of the stationary point(s) of f(x)b) How can I determine the nature of the stationary point of f(x).c) On what interval is the function f(x)... more

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Calculus

07/05/24

Antiderivative/integrals question

Find a formula for the sum of n terms. Use the formula to find the limit as n → ∞.

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Calculus

07/05/24

Antiderivative/integrals question using velocity

Use a(t) = -32 ft/sec2 as the acceleration due to gravity. (Neglect air resistance.)With what initial velocity must an object be thrown upward (from ground level) to reach the top of a national... more

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Answers •2

Calculus

07/05/24

Calculus 1 question (antiderivative/integrals?)

Find the equation of y, given the derivative and the indicated point on the curve.dy/dx = 2x - 1

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Answers •2

Calculus

07/05/24

Area under the curve problem using trig

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. (Round... more

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Answers •1

Calculus

07/04/24

Geometric series

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)10 − 8 + 6.4 − 5.12 +

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Calculus

07/03/24

The integral test

Use the Integral Test to determine whether the series is convergent or divergent.∑(from n=1 to ∞) 8/(7n-1) Evaluate the following integral. ∫ (from 1 to ∞) 8/(7x-1) dx

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Calculus

06/28/24

calculus with parametric curves

Find the distance traveled by a particle with position (x, y) as t varies in the given time interval.x = 5 sin2(t), y = 5 cos2(t), 0 ≤ t ≤ 5𝜋Find the length L of the curve.

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Answers •1

Calculus

06/28/24

Calculus with Parametric curves

At what point(s) on the curve x = 6t2 + 5, y = t3 − 7 does the tangent line have slope 1? (x, y) = ?

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Answers •1

Calculus

06/28/24

Calculus with Parametric curves

Find the exact length of the curve.x = et − t, y = 4et / 2, 0 ≤ t ≤ 4

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Calculus

06/28/24

Calculus in polar coordinates

Find the exact length of the polar curve.r = 3 cos(𝜃), 0 ≤ 𝜃 ≤ 𝜋I was only able to get to the below answer:∫from 0 to pi. √1+9sin^2(X) dx

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Calculus Math

06/27/24

Find the volume of the solid obtained by the revolving the region bounded by the graphs of the functions y = e^x, x = 2, x = 8, y = 0 about the x-axis. Draw a picture to illustrate the computation.

Show all work.

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Calculus

06/27/24

Differentials question

The measurement of the radius of the end of a log is found to be 3 inches, with a possible error of 1/2 inch. Use differentials to approximate the possible propagated error in computing the area of... more

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Answers •1

Calculus

06/27/24

Another optimization question

A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down the coast and 1 mile inland (see figure). He can row at a rate of 1 mile per hour and... more

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Calculus

06/27/24

Optimization(?) Question

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 18 cubic centimeters. Find the radius of the cylinder that produces the... more

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In exact fractional form

Help me solve this

Use the graph of f(x)=x2 below to find a number δ such that ∣∣x2−1∣∣<0.3 whenever 0<|x−1|<δ.

Find the critical points of the linear equation y = 4x^3 - 3x

What is the angle between a position vector and a tangent?

The ratio and root tests

Find the amount of oil that the field can be expected to yield during the first 6 years of production, assuming that the projection holds true

Plane Curve with Constant Angle

Finding the stationary points of a given function

Proving u and v is perpendicular to the sum of 2u and v

Stationary points of a given function

Antiderivative/integrals question

Antiderivative/integrals question using velocity

Calculus 1 question (antiderivative/integrals?)

Area under the curve problem using trig

Geometric series

The integral test

calculus with parametric curves

Calculus with Parametric curves

Calculus with Parametric curves

Calculus in polar coordinates

Find the volume of the solid obtained by the revolving the region bounded by the graphs of the functions y = e^x, x = 2, x = 8, y = 0 about the x-axis. Draw a picture to illustrate the computation.

Differentials question

Another optimization question

Optimization(?) Question

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