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1. Find dy/dx.
a) y = cosh(2x4-3/x+1)
b) y = ln(sinh-1x)
c) y = cosh(1/x)
2. Evaluate the given integral by using appropriate method in integration.
a) ∫(2x2 - 3/x2 - 3x + 2)dx
b) ∫(2x2 - 10x + 4/(x+2)2(x2+3))dx
c) ∫x3/2 ln(x2)dx
d) ∫cos(ln x)dx
e) ∫x2e-3x dx
f) -1∫2dx/(x-1)3
g) -∞∫0 (exdx/4+3ex)
h) ∫√(tan x)sec4 x dx
i) ∫(3x3/√(4-x2) dx
j) ∫(√(x2-16)/x) dx
k) ∫(dx/√(4x-x2))
3. Approximate the integral using (a) the trapezoidal approximation T4 (b) Sampson's approximation S6
1∫3(1/3x+1) dx
4. Show that k=0Σ∞(x-2)k = 1/(3-x); if 4 < x < 6.
5. Show that the given sequence is strictly increasing or strictly decreasing.
a) {n/3n+4}+∞n=1
b) {ne-2n}+∞n=1
c) {5n/n!}+∞n=1
6. Determine whether the series converges.
a) k=1Σ∞3/5k-1
b) k=2Σ∞πk+2
7. Determine whether the sequence converges; if so find its limit.
{(n+1)(n+3)/3n2}+∞n=1
8. Find the general term of the sequence.
1, -1/4, 1/27, -1/256
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Find the first derivative
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Probability distribution. The high school GPA of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories.
The dimensions of a closed rectangular box are measured as 73 cm, 67 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
gina sam and robby all rented movies from the same video store. they each rented some dramas comedies and
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Let g(x)=x^2 for rational x and g(x)=0 for irrational x. Calculate the upper and lower Darboux integrals for g on the interval [0,b] . Is g integrable on [0,b]
Recall that a graph G is randomly Eulerian from a vertex x if and maximal trail starting at x in an Euler circuit. (If T = xx_1 ... x_l, then T is a maximal trail starting at x iff x_l is an isolated vertex in G - E(T).)
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