CALCULUS I – Worksheet #8 ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1. If x = 2t – 1 and y = 3 – 4t2, then

dy

( B) − 4 t

is (A )4 t

dx

(C)

−1 4t

( D)

17 (2 − 5x)2

( E) − 4( x + 1)

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x−3 dy then equals 2 − 5x dx 17 − 10x 13 (A) (B) 2 2 (2 − 5x) (2 − 5x)

2. If y =

x−3

(C)

(2 − 5x)

(D)

2

17 (2 − 5x)

(E)

2

−13 (2 − 5x)

2

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−x 3. If y = e , then y"(0) equals 2

(B) − 2

(A)2

(C)

2 e

(E) − 4

(D)0

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e

4. If y =

lnx , then x

dy

is

(A)

dx

e

lnx

x

(B)e

2

lnx

(C)

2e

lnx

x

(D)1

2

(E)0

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5. If y =

1

then y

(iv)

x

(1) =

(A) − 1

(C) − 6

(B)2

(E) − 24

(D)24

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6. y = 5 − 2 x. Find

(A)

1

dy dx

(B)

2 5 − 2x

−1

(C)

5 − 2x

3 2 − (5 − 2x)

(D)

3

−1

2

(E)

5 − 2x

3 2 3(5 − 2x)

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7. y = x 2 + 2 x − 5 Find (A)

x +1

dy dx

(B)4y(x + 1)

y

1

(C) 2 x

2

(D)

+ 2x − 5

− (x + 1)

(E) None

3 2 2 (x + 2x − 5)

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8. y = sin 2 x. Find

dy 2 (A) − cos x dx

(B) − 2sinx cosx

(C)sin2x

(D)2cos x

(E) − 2sin x

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dy if xy + 2 x + 3y = 1. dx dy (A)2 y = x 2 ln x. Find dx

9. Find

(A)

−5

(B)

x

−y − 1 x+3

(C)

−4

(D)

x

−y − 2 x+3

(E) None

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10.

(B)x + 2x ln x

(C)x(1 + ln x)

(D)2(1 + xln x)

(E)2x ln x

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11. Find

dy dx

if y = sin

−1

(3x)

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12. If y =

3 2 x + 2x + 1, then find the derivative of y with repect to cos x.

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dy x . 13. If y = 9 , then find dx ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

14. Find

dy dx

if y = 3t

2

− 2 and x = 4t + 1.

15. Find

dy dx

if y = t

2

5 − 2 and t = 3x .

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