### Calculus

Please help me understand these problems. State the Comparison Test, the Limit Comparison Test and the Integral Test for the convergence of infinite series.

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Please help me understand these problems. State the Comparison Test, the Limit Comparison Test and the Integral Test for the convergence of infinite series.

Find the slope and the y- intercept of the following line 7y-8x-2=0

Please show in detail how to solve the series. Thank you. Does converge or diverge?

Series - problems 13 and 14.

Geometric series and limits. Please see attached.

Find the general solution of the given differential equation: (4-x)dy+2ydx=0 find the solution to the initial-valued problem (x^2+1)Y'=xe^y with initial condition y(0)=

Using 1. f(x) = , find f'(x) and then add the tangent line to the graph of y=f(x) at x = 0 2. f(x) = , find f'(x) [See attachment for equations.]

A new bridge is to be constructed over a big river. The space between the supports must be 1000 feet; the height at the center of the arch needs to be 320 feet. The support could be in the shape of a parabola or a semi-ellipse. An empty tanker needs a 250 foot clearance to pass beneath the bridge. The width of the channel for ea

#5 Let p(x) = x3 -ax, where a is constant a) If a<0, show that p(x) is always increasing. substituting in values b) If a>0, show that p(x) has a local maximum and a local minimum. c) Sketch and label typical graphs for the cases when a<0 and when a>0. Find the value(s) of x for which: a) f(x) has a local maximum

#4 What happens to concavity when functions are added? a) If f(x) and g(x) are concave up for all x, is f(x) + g(x) concave up for all x? Yes b) If f(x) is concave up for all x and g(x) is concave down for all x, what can you say about the concavity of f(x) + g(x)? For example, what happens if f(x) and g(x) are both polyn

See attached Find two linearly independent solutions of the differential equation...

See attached Determine the Taylor series expansion of the function... Use a power series method to find the complete solution of.... find two linearly independent solutions of the differential equation.... For the Bessel equation of order zero...

See attached Find the solution of.... Use Laplace transforms to show that...

(see attached for full description) 1. Find the Laplace transforms of 2. Use the Laplace transforms to solve the initial value problem y'' + 2y' - 8y = 0, y(0) = 1, y'(0) = 8 3. Solve the initial value problem y'' + 2y = r(t), y(0) = y'(0) = 0 Where r(t) = 1 for 0 <t <1 and r(t) =0 otherwise 4. Solve the initial

1. The size of a bacterial polution is 4000. Find a formula for the size, P, of the population t hours later ... 2. Abicyclist pedals along a straight road with velocity, v, .... [See the attached Question File.]

(See attachment for detailed description) When two chemicals A and B react, 1g of A and 2g of B yield 2g of C and a byproduct. The rate at which C is formed is proportional to the amount of A and B present. Suppose that at the outset there are 50g of A and 90g of B present, and that after 1 hour, 45g of C have been formed.

The following table gives the percent of the US Population living in urban Areas as a function of year2. ... 5. (a) Estimate f'(2) using the values of f in the table. ... 5. The thickness, P, in mm, of pelican eggshell depends ... 11. The quantity, Q mg, of nicotine in the body t minutes after a cigarette is smoked ... [Pl

Figure 1 shows a sketch of the curve C with equation y=cos x ln(sec x), ... (a) Find the cordinates of B in terms of e. (b) Show that the area of R is ... [See the Attached Questions File.]

See attached The shaded region R is bounded by C, the x-axis and the line x=2....

5. (a) Expand 1/sqrt(4-3x), where ... [See the Attached Questions File.]

Figure 3 shows the curve C with parametric equations ... (a) Find the value of t at the point P ... [See the Attached Questions File.]

sketch a graph of r = sin (2theta), 0<=theta<=2pi, and calculate the area of one petal, rounding to the nearest hundredth

2)Write a set of parametric equations for each of the following figures. (i) the line segment with endpoints at (3,-5) and (-2,11), such that the parameter value t satisfies 0<=t<=1. (ii)the lower half of the circle with center (-7,8) and radius 9

Following are the instructions from my teacher for the final review. please follow directions precisely and show all steps by hand. Answers must be exact unless otherwise indicated. 1) Consider the parametric equations x =2t+1/t and y = 1-t. (i) Using a table sketch the curve represented by the parametric equations. Writ

Water is the most important substance on Earth. One reason for its usefulness is that it exists as a liquid over a wide range of temperatures. In its liquid range water absorbs or releases heat directly in proportion ot its change in temperature. Consider the following data that shows temperature of a 1,000 g sample of water at

Please explain the steps in solving the questions in the attachment:

ACME Construction Company is building a suspension bridge over the Miami River. They need to know how much material will be required to construct the main support cables and what sort of cable they need to buy. The support cables will be attached at either end to the top of 100 meter tall concrete pillars. The two concrete pilla

I'm looking for help with differentiation. Please see the attached file.

How many terms are required so that you are with in 10^-3 of this limit. See the file attached.

See attached.