Calculus Answers

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question in picture

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whole question is in picture,R=4,you can sub R=4

Given f(x)=1+x+x2,

(a) Evaluate the definite integral A=∫10(1+x+x2)dx.

(b) Find the approximate An of the integral A by a sum, using n strips of equal width, and evaluate the sum.

(c) Find limn→∞An.

Find the nature of the roots of the polynomial 2x^5 + x^3 + 5x + 1

Using the ε −δ definition, show that lim 3( x -5 )=1

Find the derivative of In(1+x^2) w.r.t tan inverse x

Use simpson's method to approximate integral 0 to 8(x^2-x+3)dx with 8 such-intervals.

Expand e^2x in powers of (x-1), up to four terms

Find the intervals on which the function f defind by f(x)=x^4-8x^2+16 is concave upward or concave downward.

Find the area between the curves y^2=ax and ay^2=x^3(a>0), at the points of intersection other than the origin.