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Calculus Answers

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Find the inverse, if possible, for the following matrices.

(a) (8 -5)
11 23

(b) (5 -7 6)
-11 6 2
2 4 -7
If ∫f(x)dx within limit 0 to a=∫f(a-x)dx within limit 0 to a
Then show that
∫xsinx/(1+cos^2(x))dx within limit 0 to π=π^2/4
Q2. If A= (1 2 6),
4 11 7
9 13 3

(a) Find the minors of 1,2 and 6.
(b) Find the cofactors of 1,2 and 6.
(c) Evaluate |A|.
(d) A^-1
Find the area enclosed by the curve y^2=4x and 2x+y=4
Describe and draw a rough sketch of the level curves of the function f(x,y)=underroot (4x square - y square)
∫|x|dx within limit -1 to 2=3/2
Is the statement true or false?
Give a short proof or a counter example in
support of your answer.
The range of the function f, defined by
f(x)=e^(-x)/(1+x) on [0,∞[, is ]−∞,0[ .
Is the statement true or false?
Give a short proof or a counter example in
support of your answer.
If ∫f(x)dx within limit 0 to a=∫f(a-x)dx within limit 0 to a
Then show that
∫xsinx/(1+cos^2(x))dx within limit 0 to π=π^2/4
Prove that the function f(x) =3x^4-4x^3+5 has only one point of inflection
Find, by the first principle, the derivative of f : R → R defined by f(x) = x^3-1 at a
point x0 . Hence, find the equations of the tangent and normal to its curve at the point
(−2,−9).
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