25,270 Answered Questions for the topic calculus

Calculus

10/03/23

Limits and Discontinuity
(a) What type of discontinuity does the function 𝑔(𝑥)=1/𝑒1/x -1have at 𝑥=0(b) For which value of 𝑐 will the function 𝑓(𝑥)=(1/𝑒1/x−1+𝑐)2 have a limit at 𝑥=0?(Hint: Use one-sided limits.)(c) Using... more
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Calculus

10/03/23

Derivatives Question
Explain how you estimate the derivative in each of the following ways: As an average rate of change. As an instantaneous rate of change.
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Calculus

10/03/23

Ali, a calculus student, writes the following explanation for why the limit lim𝑥→0[𝑥^4⋅cos(2/3𝑥)] is zero
Ali, a calculus student, writes the following explanation for why the limit lim𝑥→0[𝑥4⋅cos(2/3𝑥)] is zero:Since lim𝑥→0 𝑥4=0 we conclude, from the basic limit laws,... more
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Calculus

10/03/23

AP Calculus BC - Implicit Differentiation

If xy = x + y2, find d2y/dx2
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Calculus

10/03/23

AP Calculus BC - Chain Rule
If f(3) = 4, g(3) = 2, f'(3) = -5, g'(3) = 6Find (f⋅g2)' (3)
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Calculus

10/03/23

What is the related rate of the problem
A ladder 13−−√13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.30.3 m/sec. How fast is the top... more
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Calculus

10/02/23

Calculus Homework
Find (f^-1)'(a). f(x)=5x^3+4x^2+6x+8, a=8(f^-1)'(a)=
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Calculus

10/02/23

Linear approximation of error
The distance, in feet, a stone drops in t seconds is given by d(t) =16t^2. The depth of a hole is to be approximated by dropping a rock and listening for it to hit the bottom. Assume that time... more
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Calculus Math

10/02/23

Given that f(x)=x^5h(x), h(-1)=5, h'(-1)=8, what is f'(-1)?
f(x) = x5 h(x)h(-1) = 5h'(-1) = 8Calculate f'(-1).It tells me to use the product rule, and the power rule but I can't seem to figure it out, and I've gotten multiple people to help me and I keep... more
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Calculus

10/02/23

Calculus Question
The edge of a cube was found to be 30 cm with a possible error of 0.2 cm. Use differentials to estimate:(a) the maximum possible error in the volume of the cube?(b) the relative error in the volume... more
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Calculus

10/02/23

derivative properties
suppose f'(3)=6 and g'(3) =5. Find where h'(3) =5f(x)+4g(x)+5
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Calculus

10/02/23

Calculus Question
A spherical balloon is inflated so that its volume is increasing at the rate of 2.2 cubic feet per minute.How rapidly is the diameter of the balloon increasing when the diameter is 1.1 feet? 
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Calculus

10/02/23

Calculus Question
A 16 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how fast will the foot of the ladder be moving away from the wall when the top is 14 feet above the... more
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Calculus

10/02/23

Error bound using trapezoidal and Simpson's rule
Trying to help my daughter, she is not sure how to work this.In estimating the integral -1 to 3 cos(x)dx using trapezoidal and Simpsons rule with n=4, we can estimate the error involved in the... more
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Calculus

10/02/23

Techniques of integration
Daughter is having a hard time with her homework tonight. This one is vexing her. Can someone assist in showing how to work it?How large should n be to guarantee that the trapezodial rule... more
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10/02/23

Use the Rational Zero Theorem to find all real zeros
8x3 − 15x2 + 22x + 3 = 0
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10/02/23

find all complex solutions (real and non-real).
9x3 − 17x2 + 88x + 10 = 0
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Calculus

10/02/23

Trapezodial, midpoint, and Simpsons rule
Here is a problem I can't help my daughter with. Any help is appreciated.Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the integral 1 to 7 (ln(x)/4+x)dx
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Calculus

10/02/23

Trapazoidal rule
My daughter has tried this question and looked at one similar and get get the correct answer. Can anyone show us how to work it? Thanks.Use the trapezodial rule with n=8 to approximate the... more
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Calculus

10/02/23

Midpoint rule/ttecniques of intergration numerical integration
My Daughter has tried working this problem and looked at one similar and still can't get this right. Any help is appreciated.Use midpoint rule with n-3 to approximate the integral integral of -3... more
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Calculus

10/01/23

Calculus Question
At noon, ship A is 10 miles due west of ship B. Ship A is sailing west at 19 mph and ship B is sailing north at 25 mph. How fast (in mph) is the distance between the ships changing at 4 PM?
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Calculus

10/01/23

Calculus Question
A particle is moving along the curve y=3(√4x+1). As the particle passes through the point (2,9), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance... more
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Calculus

10/01/23

Calculus Question
Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast... more
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Calculus

10/01/23

Calculus Question
A Kite 60 feet above the ground moves horizontally at a speed of 5 ft/s. At what rate is the angle between the string and the ground decreasing when 180 feet of string is out?
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Calculus

10/01/23

Calculus Question
Two sides of a triangle are 4 m and 7 m in length and the angle between them is increasing at a rate of 0.12 rad/s. Find the rate at which the area of the triangle is increasing when the angle... more
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