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[answered] MATH 1151 AUTUMN 16 WRITTEN HOMEWORK 4 NAME : OSU Name.# IN

Hi guys, I have some?trouble of solving these Calculus problems. If anyone can help me on these I will be very very grateful.

MATH 1151

AUTUMN 16

WRITTEN HOMEWORK 4 NAME :

OSU Name.#

INSTRUCTIONS : Calculators are permitted EXCEPT those calculators that have symbolic algebra or

calculus capabilities.

SHOW ALL WORK ! Incorrect answers with work shown may receive partial credit,

but unsubstantiated answers will receive NO credit. Due date : Tuesday, December 6, 2016, Recitation Class

#1 (4 pts)

Evaluate the following expressions and explain your reasoning. THINK ! (You may use symmetry and the Fundamental Theorem of Calculus!)

? (a ) 0 (c ) d 2 dx d

dx sin 5 (x )

cos 2 (x ) + 2

?x ?

2 sin 5 t ? t 0 ex

(e ) 4+ e 2x ?x ? (b) d 5 2? sin x ? x - d

dx 0 2 x3

0 sin 5 t ? t x (f ) - 1 x + 2 3 ?x 2 WH4-AU16.nb #2 (2 pts) A window is shaped as shown in figure (A) below, where f is given by

y 5 y=f(s) f (s) = 5 sin (A) 0 4 ? 32 2 s + 16 . s (Here s and f (s) are given in feet.)

The curtain is covering the window as shown in figure (B). (B) (C) Starting at time t = 0 , the curtain is being opened from left to right,

revealing the window as shown in figure (C).

Suppose that the curtain is opening at the rate of 0.8 ft sec.

Find the rate at which, A, the area of the exposed part of the window

is changing when t = 4 sec.

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