## [answered] 1) Calculate f(g(1)), given that (a) - 8/9 2) Find the slop

I need some help with my calculus homework please..

1) Calculate f(g(1)), given that (a) - 8/9 2) Find the slope of the tangent line to the graph of f at x = 4, given that (a) -8 3) Determine (a) (b) 7/3 (b) (c) - 10 x

f ( x ) 2 x 2, g ( x ) 2 x2 2 (c) -9 2x3 x

lim

x 4 x 5 2 x 2 2 (b) 0 (d) (c) 4/3 (e) . - 2/9 (d) -5 (e) -7 (d) 3/10 (e) 1 f ( x ) x 2 4 x . . 1/2 4)

Let f(x) = x3. A region is bounded between the graphs of y = -1 and y = f(x) for x between

-1 and 0, and between the graphs of y = 1 and y = f(x) for x between 0 and 1. Give an integral that

corresponds to the area of this region.

(a)

(b)

(c)

1

1

1

3

3

3 (1 x )dx

2(1 x )dx

2(1 x )dx

1 (d) 1 (1 x

1 5)

a) d) 6)

a)

c)

e) 0 (e)

3 1 )dx ( 1 0 0 x 3 )dx Given that 5x3 - 4xy - 2y2 = 1, determine the change in y with respect to x.

b)

c)

2

2

15 x 4

15 x 4 y

15 x 2 4 4 4y 4 4y 4x 4 y

10 x 4 y 4x 2 e) 15 x 2 4 y 4x 4 y Compute the derivative of - 4 sec(x) + 2 csc(x).

- 4 sec(x) tan(x) - 2 csc(x) cot(x)

b)

- 4 csc(x) - 2 sec(x)

- 4 (sec(x))2 - 2 (csc(x))2

d)

- 4 sec(x) tan(x) + 2 csc(x) cot(x)

- 4 (tan(x))2 - 2 (cot(x))2 7) Determine d 4x 4 2x dx 4 x 4 2 x a) b) 2 24 x 1

( 4 x 3 2) 2

d) c) 2 48 x 1

( 4 x 3 2) 2

e) 2 12 x 2

( 2 x 3 1) 2 6x 2

( 4 x 3 2) 2 24 x

( 4 x 3 2) 2

8)

a) Determine the concavity of the graph of f(x) = 3 sin(x) + 4 (cos(x))2 at x = .

8

b)

- 10 c)

4

d)

-8

e)

-6 9) Compute 4 x

a) d) 2 x 3 4dx 8 3

( x 4) 3 / 2 c

3 4

3 b) e) 1

x3 4 c 16 3

( x 4) 3 / 2 c

9 c) 8 3

( x 4) 3 / 2 c

9 8

1

c

3 x3 4 10) Give the value of x where the function f(x) = x3 - 9x2 + 24x + 4 has a local maximum. a) 4 11) The slope of the tangent line to the graph of 4x2 + cx - 2 ey= - 2 at x= 0 is 4. Give the

value of c.

-2

b)

4

c)

8

d)

-4

e)

-8 a)

12)

a) b) -2 c) 2 d) -4 e) 3 What is the average value of the function g(x) = (2x + 3)2 on the interval from x = - 3 to

x = -1?

7/3

b)

-4

c)

5

d)

14/3 e)

3 13) Compute 1 1 tan t tan 4 4 lim t 0

t b) a) 1 .25* c) d) 14) Find the instantaneous rate of change of 2 e) -1 at t = 0. f (t ) 2t 3t 4 t 3t 4

a) -3 b) 15) Compute - 3/4 c) 0 3 2 d) -4 e) - 5/4 d) -2 e) undefined 4x

x lim x 0 sin( 2 x ) cos(2 x ) a) 16) Given y &gt; 0 and a)

17) b) 0 c) - 5/2 dy 3x 2 4 x dx

y then what is y when x = 0?

3

b)

2

c) 1 . If the point is on the graph relating x and y,

(1, 10 ) d) 6 e) 10 a) A particle's acceleration for t &gt; 0 is given by a(t) = 12t + 4. The particle's initial position

is 2 and its velocity at t = 1 is 5. What is the position of the particle at t = 2?

10

b)

12

c)

16

d)

4

e)

20 18) Determine /2 0 b) . /6 sin( 3 x )dx cos(3 x )dx

0 a) -1 1 c) 0 19)

a)

c)

e) Determine the derivative of f(x) = (cos (2x - 4))3 at x= /2.

- 6(cos( - 4))2

b)

- 6cos( - 4)2 sin( - 4)

2

- 6(cos( - 4)) sin( - 4)

d)

18(cos( - 4))2 sin( - 4)

18(cos( - 4))2 20) Determine d

ln(ln( 2 cos( x )))

dx d) 2/3 e) - 2/3 a) c) cos( x )

( 2 cos( x )) ln( 2 cos( x ))

sin( x )

( 2 cos( x )) ln( 2 cos( x )) e) 21) b) d) sin( x )

ln( 2 cos( x ))

sin( x )( 2 cos( x ))

ln( 2 cos( x )) cos( x )

ln( 2 cos( x )) a) Give a value of c that satisfies the conclusion of the Mean Value Theorem for Derivatives

for the function f(x) = - 2x2 - x + 2 on the interval [1,3].

9/4

b)

3/2

c)

1/2

d)

2

e)

5/4 22) The derivative of f is graphed below. a) Give a value of x where f has a local maximum.

-4

b)

-1

c)

- 5/2 d)

There is no such value of x. e) 1 23) Let 1)

2)

3)

4)

a) Which of the following is (are) true?

f is continuous at x = -2.

f is differentiable at x = 1.

f has a local minimum at x = 0.

f has an absolute maximum at x = -2.

2 and 4

b)

3 only

c)

2 only 24) Given x 5 x 2 f ( x ) x 2 1 2 x 1 2x3 1 1 x 50 50 0 2 3 f ( x)dx 3, -3 c) , determine f ( x )dx 4 1 and 3

2 e) 1 and 4 . f ( x)dx

0 a) 10 25)

a)

d) Give the approximate location of a local maximum for the function f(x) = 3x3 + 5x2 - 3x.

(- 1.357, 5.779)

b)

(0.2457, - .3908)

c)

(- 1.357, 5.713)

(0.2457, - .3216)

e)

(- 1.357, - .3908) 26) A particle moves with acceleration a(t) = 3t2 - 2 and its initial velocity is 0. For how many

values of t does the particle change direction?

3

b)

2

c)

1

d)

0

e)

4 a) b) d) There is not enough information. d) -6 e) 5

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