Calculus Answers

Find the Maclaurin series for the function f(x) = square root of

(x²+2-x)⁵

When a particle is located a distance x meter from the origin, a force F( x )(newton) acts on it. Given F'(x) = 16.3.arctan(x - 8.5), F(8.5)=0. How much work is done in moving it from x=0 to x=8.5.

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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

2y = 4sqrt(x), y=5 and 2x + 2y =6.

There is a line through the origin that divides the region bounded by the parabola 

y = 6x - 7x² and the x-axis into two regions with equal area. What is the slope of that line?

Find the center of mass for each of the following regions.

1. The region bounded by y = x^3 ,x = -2 and the x-axis.

Provide all detailed steps to find the limit of the following functions.

Lim x→∞ (e^4x - e^-2x) ÷ (ln(x+1)

F(x) = 2x³ + cx² + 2x.

Suppose f is differentiable on R and has two roots. Show that f' has at least one root.

1. The demand for a product, in dollars, is P = 2000 - 0.2x - 0.01x²

Find the consumer surplus when the sales level is 250.

2.1. Find the area of the region that lies inside the circle r = 3sin(x)and

outside the cardioid r = 1+ sin(x).

2.2 Find the length of the cardioid r = 1+ sin(x)

1.Find the Maclaurin series for thefunction f(x)= (x^2+ 2-x)^5/2and its radiusofconvergence

f(x,y)= -(x²-1)²-(x²y-x-1)²

Find the critical points of f (x, y) and Using the Second Partials Test (SPT), find the relative extrema’s of f (x ,y)