# Assorted Calculus Questions

Below are the graphs of four functions. Which function is invertible?

Set up the integral for the length of the smooth arc y = e x on [0, 10].

What is the area of the triangle bounded by the lines x = 1, y = x − 1, and y = 3 − x ?

Suppose that a bicyclist is biking with a velocity function of v (t) = 2t − 1 ft / min. Starting at t = 0, how long does it take the bicyclist to go 30 ft?

What does sech (0) equal?

What is the area between the curve g (x) = 3x 2 + 2 and the x-axis from x = −2 to x = 0?

You are throwing paper airplanes in class, and you throw them hard enough they start out at a horizontal speed of 10 ft / s. However, they have a horizontal deceleration of 4 ft / s. What is the greatest distance away from the intial position that an object can be if it can be struck by the airplane?

What is the area of the region bounded by the curves y = x 3 − x and y = 7x − x 3?

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#### Solution Preview

y=arcsin(0.5)=

Below are the graphs of four functions. Which function is invertible?

k(x) is invertible as it is strictly decreasing with increasing of x.

Set up the integral for the length of the smooth arc y = e x on [0, 10].

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#### Solution Summary

The solution gives detailed step on solving 23 calculus questions. The main topics include inverse of function, derivative, integral.