(10 pts) For every linear function f(x) = ax + b.

1) (10 pts) For every linear function f(x) = ax + b.
a) Is the function always “one-to-one” for all b’s if a > 0 ? (justify your answer)

b) Is the function always “one-to-one” for all a’s if b > 0 ? (justify your answer)

2) (10 pts) Show that the function f(x) = e^(-x) is “one-to-one”

3) (10 pts) Fill in the blanks. If the graph of f(x) goes through the point (3,4) and f^'(3) = -5, then the graph of f^(-1)(x) goes through the point (___ , ___) and (f^(-1))’ (___)= -1/5?

 
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find the exact values of (a) sin(θ)

5) (10 pts) For θ = arctan(3/2), find the exact values of (a) sin(θ), (b) cos(θ), (c) csc(θ), and (d) cot(θ).
6) (10 pts) Let dθ/dt=5 deg/sec when θ = 50 deg and θ and h are related by tan(θ) = h/40 . Find dh/dt . h is in feet. t is in sec. Convert degrees to radians as the first step to doing the problem. Include units in your answer.

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For which positive integers n is f(x) = x^n

For which positive integers n is f(x) = x^n “one-to-one”? Justify your answer.
Please help?! My professor is being confusing and very generic. I’m confused at how I’m supposed to answer this and also justify it.

Thank you in advance.

 
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Discuss with your classmates how you would graph

Discuss with your classmates how you would graph f(x) = ax + b/cx
+ d. What restrictions must be placed on a,b,c and d so that the graph is indeed a transformation of y = 1/x?

 
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Use the given pair of functions

Use the given pair of functions to nd and simplify expressions for
the following functions and state the domain of each using interval notation.
(g◦f)(x) (f ◦g)(x) (f ◦f)(x)

-f(x) = 2x + 3, g(x) = x2 −9

 
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Evaluate the following integrals

Evaluate the following integrals.

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In problems 1 – 10, calculate the Taylor polynomials

In problems 1 – 10, calculate the Taylor polynomials P0 , P1 , P2
, P3 , and P4 for the given function centered at the given value of c. Then graph the function and the Taylor polynomials on the given interval.

Question #6)

f(x) = x , c = 9, [0, 20]

 
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Please help with this questions for a 4 part quiz

Please help with this questions for a 4 part quiz that I’m taking. Thank you.
Q5.) Suppose in Figure 6 (10.3 #14) Suppose in Fig. 8 we begin with a circle of radius = 1(A1 = ) and construct 2 more circles inside, each with radius ½. Continue the process of constructing two new circles inside each circle from the previous step and find the total area of all of the circles. Sum = A1 + A2 + ….

 
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In problems 1 – 14, use the substitution method

In problems 1 – 14, use the substitution method and a known power series to find power series for the given functions.

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Please help with this question

Please help with this question. My professor said I approached it the wrong way.
“Please calculate the first several terms of the Maclaurin series for the given functions and compare with the series representations we found in Section 10.9 . (The series should be the same.)”

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