Calculus Answers

Which of the following could be an example of a function with a range


and a domain

where a > 0 and b > 0?

Find the domain of the function defined by f(x) =√(9x³-x⁴)

Let
f
(
x
)
=
x
4
−
2
x
2
f(x)=x4−2x2
. Find the all
c
c
(where
c
c
is the interception on the x-axis ) in the interval (-2, 2) such that
f
′
(
x
)
=
0
f′(x)=0
. ( Hint use Rolle's theorem )

Differentiate
tan^-1{(sinx-cosx)/(sinx+cosx)}
with respect to x/2

If f(x)=(4x^2-7x-2)/(x-2), x not is equal to 0
Find a delta > 0 such that
|f(x)-9|< 1/100 for 0<|x-2|<delta.
Hence show that lim x->2 f(x)=9

Find the intervals in R over which integration of (t+1)^3 e^t dt within limit -1 to x is decreasing

integrate
x√(a^2-x^2)/(√a^2+x^2) dx

If y= e^(m tan^-1x) show that
(1+x^2)yn+1 + (2nx-m)yn + n(n-1)yn-1=0

Integrate( x^2+1)dx/(2x+1)(x-1)(x+1)

Integrate 1/(x^2-6x+11)dx within limit -5 to 5