5 - Differentiation Questions Answers
d/dx((1+x^2+x^4)/(1+x+x^2))=ax+b
then a=?, b=?
1+x2+x4 = (1+x+x2)(1-x+x2)
now solve
since first one is a straight line so at every point only one tangent is possible so it is differentiable
but second one which is modulus has a sharp turn at x = -5/2 so two tangents at x = -5/2 are possible so is not differentiable.
lim ∑ nr=1 1/n er/n n tends to infinity.
limn->∞ ∑r=1n er/n/n
This question is related to definite integration, consider 1 and divide it into n parts, upto nth part total value = r/n is equivalent to x and 1/n is dx
so question will be
0∫1 exdx
now solve it
if f(X)=xlxl then find f-1(x) can you please explain me the meaning and use of sgn
f(x) = x|x| => f(x) = -x2 for negative real values of x and f(x) = x2 for positive real values of x
so f-1(x) = -√|x| for negative real values and = +√|x| for positive real values of x
which of the following is differntiable at x=0 ?
cos(lxl)+lxl
sin(lxl)-lxl
sin(|x|)+|x| is differentiable at x = 0
LHD of first = {cos|0+h|+|0+h|-cos|0|-|0|}/0+h-0 = (cosh+h-1)/h = (1-2sin2h+h-1)/h = 1 (on taking limits)
now check RHD, its value will be -1
similarly in second both values are 0 so it is differentiable