# Calculus Problems

## Transcribed Text

Question tilhat is: Sintcos-l(x)) \$ 1-* B)ffi C) 1-x L D)- Qus\$st 4 Evaluat€ the sum: f n(a + f) n*L A) 10 B) 18 c) 20 D) 40 Question 5 Apply substitution : x=6'tan(0) 1 to simplify an expression ffi v5 A) ;;"r-(e) B) 5'Cos{0} L C) = Cos(o) vf, o)# 12 10 A) B) c) D) Question 2 A 6 pound object stretches a spring 3 inches' How much work is required to stretch this spring from 3 to 5 inches? L6 Question 6 Rewrite sum using sigma notation sta*ins with k = 1' -|+; -; - t n) xLr? el Etr# c) Xtr(*l)n# D) XEr(-Dn* Question 3 Find derivative of arc tan (rff) 1 A)- ' !+xt 1 B)- ' 1-+xc 1, ta\ * "t 2.fi7t+x1 x D)- ' 1-+xz Question 7 Find all values of x for which the given geometric series convefges: f r,, -:t- L\z ) k=1 0(x(1" 2<x<5 L<x<3 0<x<3 A) B) c) D) I Question s I Find nartial sum Sa for the foltowing series: lo x'*#) A)2 B)1 c)0 D)1,2 I Question s I t, tni, sequence converges or diverges: I l{#} A) converges B) diverges C) neither que\$tion 10 Calculate the value of total sum for the following infinite series: 111 1+-+-+-+... 4 t6 64' ! 3 2 : 4 3 A) B) c) D) See next page Quesfon 11 Evaluate the integral: fx2 J.;.rya* Question 12 A rylindrical tank with radius 3 feet and height I feet is filled completely with a water How much work it will take to pump all of the water over the top edge of the tank? Specific Aravity of water is 62 poundslft3. Question 13 Evaluate the integral: r dx- tJ x2+ 2x*10 Question tlt Apply integration by part: f I xzCos(x)dx J Question 15 Use partial fractions decomposition to find the integral: rSxz+x*L2 t- J x3 +4x Question 16 Evaluate the integral: 1t r I Coss(7r) dr J 0 See next page Question 17 Use the Ratio Te\$t to determine if the series absolutely convergent: 6 s-r 22 )- /-t n! }'.=t que\$tion 18 Calculate the Taylor polynomial (first three terms only) for the function f{x} * ln(x) at th€ poilt c ='2. Question 19 Find a bound for the'errof of apprsximation function f(x) = Cox(x) with polynomial Pl{x) on interual l-r\$12, N121. (See example 3 in section 10.11, page 4) qu€ctioa 20 tlow many terms of Taylor series are needed to apptoximate f(x) = gI within 0.001 on interval [0, 2I.

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