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Check the continuity of the function
f: R^2to R at(0,0) , where f is defined by
f(x,y)= e^(2x+y) + tan x
Find the domain and range of the function f, defined by :
f(x,y,z) = x/(2y-3z) : x,y,z∈ R
Let f: R^2 to R be a function defined by
f(x,y,z) = { 1/(x-1) + 1/(y-1)+1/(z-1);
x≠1,y≠1,z≠1
{ 0 ; Otherwise
Calculate fxz(1,1,1)
Apply Young's theorem to justify that
fxy(1,1)= fyx(1,1)
for the function f: R^2 to R , defined by
f(x,y) = | x+ y|
State Bonnet’s mean value theorem for integrals. Apply it to show that:
|3∫5 cosxdx/x|≤ 2/3
if the power series ∑n=1 ∞ a n x^n converges uniformly in ]alpha,beta[,then so does∑n=0 ∞ an(-x^n) true or false ?justify.
Find the derivative of the fun
tion
f(x) = 15 − x
√
6x + 1 +
x
1 + x
.
[1℄ − √
9x+1
6x+1 +
1
(1+x)
2
[2℄ − √
3x
6x+1 +
√
6x + 1 + 1
(1+x)
2
[3℄ √
3x
6x+1 + 1
(1+x)
2
[4℄ √
9x+1
6x+1 +
1−2x
(1+x)
2
Dierentiate the fun
tion
f(x) = 3x
3
e
2x
.
[1℄ 5x
4
e
3x
[2℄ 3x
2
e
2x
(x − 3)
[3℄ 3e
3x + 9x
4x
5
[4℄ 3x
2
e
2x
(2x + 3)
Find the number “ c ” that satisfy the Mean Value Theorem (M.V.T) on the given
intervals.
(a) f(x)= e-x , [0, 2]
(b) f(x)= x/(x+2), (1,
tan(x-y) = y/(1+x)
