Let
then,
Let
then,
Let
then,
Let
then,
For the function
f(x, y) = x^{3} + y^{3}  3x — 12y + 20 has,
The g 1({0}) for the function g(x)= ⌊x⌋ is ___________
g({0}) for the function g(x) is {x  0 ≤ x ≤ 1}. Put g(x) = y and find the value of x in terms of y such that [x] = y.
The function f(x) = has
irremovable discontinuity.
If f(x) = then
(i)f(x) = 1
(ii) f(x) = 2
(iii) f (x) =2
Q. Which of these statement(s) is/are correct?
Given that
Clearly , the value of function is changing at x = l, therefore, we check limit at x = l
and
If f(x) = (x^{2}  1) x^{2}  3x + 2  + cos (x), then set of point of non  differentiability is
Given that
Clearly, the rule of the function is changing of x = 1 and 2. So, we shall test the differentiability of f(x) only at the points x = 1, and 2
Clearly Rf'(1) = Lf'(1) and Rf'(2) ≠ Lf'(2) Hence ,f(x) is not differentiable at x = 2.
If f(y) = then f(x) is
Given that
Clearly f(x) is discontinuous for
Let us consider the pair of ordered pair of sequences
(a_{n} , b_{n}) and (c_{n}, d_{n}) such that
= (a,b) and (c_{n}, d_{n}) = (a,b), then does not exists, if
Let
then,
Let
then,
Let
then at (0, 0)
Let
then,
Consider the function f(x) = x^{3} where x is real, then the function f (x) at y = 0 is
Given that
It is clear that the funtion is twice differentiable at x = 0 and the other points the function is a polynomial.
Therfore, it is obviously differentiable.
If f(x) = then
Given that
Similarly, Lf'(0) = 0
Hence f(x) is differentiable at x = 0.
Let f : [0, 10] → [0 ,10] be continuous function then
The derivative of a periodic function with period T is
f(x) = x x, then choose the correct statement








