Calculus Answers

A particle starts from rest (that is with initial velocity zero) at the point x = 10
and moves along the x-axis with acceleration function a(t) = 12t. Find the
resulting position function x(t).

Let C denote the circle whose equation is (x − 5)2 + y
2 = 25. Notice that the
point (8, −4) lies on the circle C. Find the equation of the line that is tangent
to C at the point (8, −4).

-Find the derivative of f(x) = -4x2 + 11x at x = 10.

-Find the derivative of f(x) = negative 9 divided by x at x = -8.

-Find the derivative of f(x) = 8x + 4 at x = 9.

-Find the derivative of f(x) = 4 divided by x at x = 2.

-The position of an object at time t is given by s(t) = -4 - 2t. Find the instantaneous velocity at t = 6 by finding the derivative.

find all of the exact solutions of the equation and then list those solutions which are in the interval [0, 2π)

sin(x)^2 = 3/4

-The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the derivative.

-Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 7 squared as x approaches 7.

The publishers of a business magazine are running a sales promotion for their weekly magazine. The number of prospective customers a sales representative sees per day varies from 1 to 40. The table shows the simulated data of the number of prospective subscribers approached by a sales representative for 8 consecutive weeks.

Day 1 2 3 4 5 6 7
Week 1 20 22 27 17 31 12 39
Week 2 26 13 30 18 24 14 32
Week 3 21 12 22 37 30 23 18
Week 4 15 33 10 28 34 24 22
Week 5 11 33 21 32 26 19 22
Week 6 19 27 20 18 31 14 37
Week 7 29 22 27 30 16 09 36
Week 8 08 28 19 28 25 36 26
If the sales representative is able to get 20% of the prospective customers to subscribe, the maximum expected number of subscriptions per week is . If the sales representative earns $3 per subscription in addition to daily wages, the minimum expected value of the extra income per week is .

1) By using the formula, f^' (x)=lim┬(z→x)⁡〖(f(z)-f(x))/(z-x)〗, find the derivatives of the following functions.

a) f(x)=1/(x+2)
b) f(x)=1/((x-1)²)
c) g(x)=x/(x-1)
d) g(x)=1+√x

1. By using the formula, f^' (x)= lim┬(z→x)⁡〖(f(z)-f(x))/(z-x)〗, find the derivatives of the following functions.

a) f(x)= 1/(x+2)
b) f(x)= 1/((x+2)²)
c) g(x)= x/(x-1)
d) g(x)=1+√x

A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.

what is the maximum number of relative extrema contained in the graph of this function?

f(x)=3x^3-x^2+4x-2