25,270 Answered Questions for the topic calculus

Calculus

08/26/23

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by: y = sin(x), y = 0, 0 ≤ x ≤ 𝜋; about y = −3

I know it is integrating from 0 to pi, but the line that it is rotating around is confusing me a bit. The answer I came up with was integrating from 0 to pi of pi times (sin^2x+6sinx+9), which is... more
Calculus

08/25/23

Use version 2 of the arc length formula to find the length of the curve defined by

Use version 2 of the arc length formula to find the length of the curve defined by 16xy^2 - y^6 = 8 from (9/16, 1) to (9/8, 2) x = 1/2y^2 + y^4/16dy/dt = -1/y^3 + y^3/4integral sign upper bound 2... more
Calculus

08/23/23

calculus for life science

Find the slope and the equation of the line tangent to  f(x)=2x−1x+9  at x​ = 1.The slope of the line tangent to​ f(x) at x​ = 1  is enter your response here.Answer the following... more
Calculus

08/23/23

calculus for life science

The height of a ball t seconds after it is thrown from the top of a building is given by H(t)=−16t2+47t+122. Find its​ height, velocity, and acceleration 3 seconds after it is thrown from the... more
Calculus

08/23/23

calculus for life science

The median weight of a boy whose age is between 0 and 36 months can be approximated by the functionw(t)=8.17+1.96t−0.0091t2+0.000091t3​,where t is measured in months and w is measured in pounds.... more
Calculus

08/23/23

calculus for life science a6.9

The position of a particle moving along a coordinate line is s=57+4t​, with s in meters and t in seconds. Find the rate of change of the​ particle's position at t=6 sec.The rate of change of... more
Calculus

08/23/23

cosine limits??

lim x-> infinity (cos(5x/x^2+7 )+pi/3)Will this be DNE because the cosine graph keeps oscillating from positive and negative?
Calculus

08/23/23

Limits of a natural log

lim x-> 2 [ln(x/e^x-1)]Do I use direct substitution ? How do I do the next step after that?

08/21/23

A wood that is 120 inches in length is to be cut into two parts such that the ratio of the parts constitutes the Golden Ratio. What must be the lengths of the wood?

A wood that is 120 inches in length is to be cut into two parts such that the ratio of the parts constitutes the Golden Ratio. What must be the lengths of the wood? is 74.16 and 45.84 correct?

08/21/23

If Jefferd wants the width of the frame to be 1-foot long, what should be length of the frame? Use 1.618 as the value of the Golden Rectangle. 

Jefferd wants to send his picture to Jessy. He wants the picture frame to be a golden rectangle so that he will look good in it. If Jefferd wants the width of the frame to be 1-foot long, what... more
Calculus

08/21/23

Which curve bends more sharply?

Two curves, y = f(x) and y = g(x), run through the point P(x0,y0). You know that f'(x0) = 0, f''(x0) = 3, g'(x0) = 3/4, and g''(x0) = 5. Which curve bends more sharply in P? Calculate the rate of... more
Calculus

08/20/23

Please help soon!

A curve is given by x5-x4y4+y5=-1507 If y(-3)=2 evaluate dy/dx
Calculus

08/20/23

For the function, identify the holes, intercepts, and horizontal asymptote. Then sketch the graph.

f(x)=(x^2 +4x)/(-3x^3 3x^2 +18x)
Calculus

08/20/23

Solve the equation; include extraneous solutions(if avalible)

1/5=4/5+4/5r
Calculus

08/20/23

Solve each equation. Round your anwsers to the nearest ten-thousandth.

5^6m +8=92 e^n+8.2 +5=0
Calculus

08/20/23

Use identities to find the value of each expression

Find Cot theta and Tan theta if (Sin theta=1/3) and (Cot theta>0) Find Csc theta and Sec theta if (Cot theta=-5/2) and (Sin theta>0)

08/20/23

If you have a wooden board that is 0.75 meters wide, how long should you cut it such that the Golden Ratio is observed? Use 1.618 as the value of the Golden Ratio.

If you have a wooden board that is 0.75 meters wide, how long should you cut it such that the Golden Ratio is observed? Use 1.618 as the value of the Golden Ratio. I just multiplied them, but... more
Calculus

08/19/23

Please help me!

Find the point on the line 2x+5y-5=0 which is closest to the point (-4,-1).
Calculus

08/19/23

Please help with the rest of this

An open-box (top open) is made from a rectangular material of dimensions a=12 inch by b=11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine... more
Calculus

08/19/23

I dont understand this

Calculus

08/19/23

Please help with this

Find the point on the curve y=4x+4 which is closest to the point (4,0).
Calculus Math

08/18/23

Limit of Cosine

lim as x approaches infinity Cos(x)I'm pretty sure it doesn't exist, but my assignment doesn't like that answer
Calculus

08/18/23

Estimate the instantaneous rate of change for g(x) = 2/(x+6).

Estimate the instantaneous rate of change for the function g(x) = 2/(x+6) at the point where x = 3.Use a TI-83 (or 84) to calculate the slopes of secant lines as x gets close to 3. Use the table... more
Calculus Math

08/18/23

bacteria popluation growth

Example. A bacteria population experiences exponential growth with a constant growth rate of r. After 4 hours, the population increases by 30%. When will the population double?Solution: We will... more
Calculus Math Econometrics

08/18/23

Compound interest

You invest $1500 into an account which has interest compounded continuously at a fixed rate. After 2 years, the account has $2200. After how many years (from the time of the original investment)... more

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