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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
An economy has three sectors: A, B, C. Sector A sells 20% of its output to B and 30% to C and retains the rest. Sector B sells 30% of its output to A and 40% to C and retains the rest. Sector C sells 50% of its output to A and 30% to B and retains..
Application of matrices in real word problems -Five neighborhoods ( NB ) all want to raise money for a playground for their kids.
Environmentalists are always concerned about endangered species. It's a lucky thing that environmentalism itself is a new thing-those people want to interfere with the natural process of evolution.
Show that any complex number z with |z| = 1, other than z = 1, can be expressed as with an appropriate choice of the real parameter t.
Let A be the area under the graph of an increasing continuous function f from a to b, and let Ln and Rn be the approximations to A with n subintervals using left and right endpoints, respectively.
What is the landing space per step
A spring with a 2 kg mass attached to it has spring constant 8 N/m and no damping. There is an external force given by F(t) = 24 sin 2t N, where t is time. The mass is initially stretched 2 m beyond the equilibrium position and released with an in..
Let x, y be elements in the Boolean algebra B. Prove that x = y if and only if xy + xy = 0. How many rows are needed to construct the (function) table for a Boolean function of n variables?
The radius of a circular disk is given as 26 cm with a maximum error in measurement of .2 cm. Use differentials to estimate the maximum possible error in the calculated area of the disk.
1. Consider R3with two orthonormal bases: the canonical basis e=(e1,e2,e3) and the basis f=(f1,f2,f3), where f1=(1,1,1)/(3^(1/2)) ,f2=(1,-2,1)/(6^(1/2)) ,f3=(1,0,-1)/(2^(1/2))
Find the error in the linear approximation to the value of f(3 + 0.06) that we found in part b). Find the percentage that results from approximation f(3 + 0.06) by the value in part b).
Find the quadratic polynomial of best fit and graph it on the scatterplot. State the formula for the quadratic polynomial.
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