144 Answered Questions for the topic Question

#### Calculus 1- Question Involving Riemann Sums

Use Riemann sums and limits to find the area under the given function on the given interval. f(x) = x+1, [0,2]

#### Calculus 1- Question involving Riemann Sums

Use a calculator or computer to compute the left and right endpoint Riemann sums for the given function over the given interval with the specified number of equal intervals. (a) f(x) = x+1,...
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#### Calculus 1 - Question Concerning Optimization

A rectangle is to be inscribed in a half circle of radius 1 ft. what dimensions will give the largest area?

#### Calculus 1 - Optimization

1. You are to make a box without a lid from a 100 cm by 35 cm piece of cardboard. What are the dimensions that will maximize the volume? What is the maximum volume?

#### Calculus 1 Question concerning Concavity

Give an example showing that a function can be concave up on its entire domain and yet never achieve a minimum value.

#### Calculus 1- Concave up or down and inflection

Find where the following function is concave up and where it is concave down. Where are the inflection points of the function? f(x) = cos(2x)

#### Calculus 1- Concave up or down and inflection

Find where the following function is concave up and where it is concave down. Where are the inflection points of the functions? g(y) = tan(y)

#### Calculus 1- Mean Value Theorem

Use the Mean Value Theorem to prove that if h(z) is continuous on a closed interval [a, b] with h′(z) = 0 for all z ∈ (a,b), then h(x) = h(y) for any x,y ∈ [a,b].

#### calculus 1- Question involving Mean Value theorem

A rectangle is to be inscribed in a half circle of radius 1 ft. what dimensions will give the largest area?

#### calculus 1- Mean Value Theorem

In each part of this problem a value for a function f(x) at a is given, a range for the derivative of f (x) on (a, b) is given, and a possible value for f (b) is given. Assuming that f (a) is...
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#### Calculus 1- Mean Value theorem Question

show that the point c between a and b guaranteed by the mean value theorem is always a+b/2 for any a, b, and any quadratric function.

#### Calculus 1- Extreme Value of functions

A rectangle is to be inscribed in a half circle of radius 1 ft. what dimensions will give the largest area?

#### Calculus 1 - Related Rates problem (draining tank)

Water is draining from a right cylindrical tank at 5 l/s. The tank has a radius of 4 m and is 15 m tall. How fast is the height of the water changing when the height of the water in the tank is 7 m?
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#### Calculus 1- Related Rates Problem(Draining Tank)

Water is draining from a right cylindrical tank at 5 l/s. The tank has a radius of 4 m and is 15 m tall. How fast is the height of the water changing when the height of the water in the tank is 7 m?
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#### Calculus 1- Related Rates Problem

Water is draining from a right cylindrical tank at 5 l/s. The tank has a radius of 4 m and is 15 m tall. How fast is the height of the water changing when the height of the water in the tank is 7 m?
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#### calculus 1 Question Rate of Change

Let θ be an angle that is not a right angle in a right triangle. If the ratio of the length of the adjacent side to the opposite side is increasing at a rate of 1/3 s−1 when the lengths of the two...
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#### Implicit Differentiation Calculus 1 Question

assume that y=f(x) has an inverse on an interval around x = a and that f'(a) = 0 why does f^-1(y) not have a derivative at y = f(a)?

#### Calculus 1 finding Unit Vector Position

In the following r(t) is the position of an object as a function of time. Find a unit vector in the direction of travel at the given ta) r(t) = (5t + cos(t), t sin(t), e^t), t = 0

Question Math

02/10/21

#### Calculus finding left and right limits at the following points

Find the left and right sided limits of the following functions at the given point. Are the functions continuous at the point? (a) f(x)=x^2+2, x=1

#### Calculus 1 Using Definition of derivatives

Assume that g(y) has a derivative at y = 3.5 with g′(−3.5) = −3. Using the definition of the derivative, explain why the function f (y) = g(y) − 10 has a derivative at y = 3.5 with f′(3.5)=−3....
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#### Calculus 1 Question Estimating Derivatives

The following functions have derivatives at the given points. Estimate the derivative to two decimal places using a numerical technique. f (x) = x^1/3, x = 4

#### Calculus 1 Question Derivatives

1)Assume that g(y) has a derivative at y = 3.5 with g′(−3.5) = −3. Using the definition of the derivative, explain why the function f (y) = g(y) − 10 has a derivative at y = 3.5 with f′(3.5)=−3. ...
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#### Calculus 1 Question Derivatives

Explain why the following functions do not have derivatives at the designated points. a) f(x) = |x−1|, x = 1

#### Calculus 1 Question- linear approximation

The volume of a sphere with radius r is V(r) = (4/3)(π)(r^3). Use a linear approximation for V (r) at r = 2 to approximate the volume of a sphere with radius r = 1.94. What is the error in this...
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#### Calculus 1 Question

Given are a function, an a, and a b. Use this information to approximate f (b) using the value and the derivative of the function at a. f (x) = 3x + 3, a = 2, b = 2.5

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