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Calculus

Math 150 Exam 3

Differentiate.

1. y = (2 + x)√x

2. k(r) = e r – r e

3. F(t) = At / (Bt2 + Ct3)

4. f(t) = t sin πt

5. J(θ) = cot 2 (nθ)

6. R(t) = arcsin (1 / t)

7. y = ln (csc x – tan x)

8. y = (√x) x

9. y = tan-1 (x2)

10. y = (sin x)ln x

Find the limit. No L’Hospital rules since we did not learn yet.

11. lim (sin Ax) / (sin Bx) (A > 0, B> 0)
x -> 0

12. lim (1 + ax) b / x
x -> 0+

13. A particle moves according to a law of motion s = f(t).

f(t) = t2 e –t

(a) Find the velocity after 1 second.
(b) Find the acceleration after 1 second.

14. At noon, ship A is 150 km west of the ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 pm?

15. Find the linearization L(x) of the function at a.

f(x) = sin x, a = π/6

16. Find the differential of y.
(a) y = ln (sin θ)
(b) y = 2x

17. Find y”.

y = tan θ sec θ

18. Find y ‘ by implicit differentiation.

cos(xy) = 1 + sin y

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