Theorems for Differentiability
Trending Questions
Q. Let f(x+y)=f(x)+f(y) and f(x)=x2g(x) for all x, yϵR, where g(x) is continuous function. Then f′(x) is equal to
- g'(x)
- g(0)
- g(0) + g'(x)
- 0
Q. Let g(x) = x.f(x), where f(x) = f(x)={x sin1x, x≠00, x=0. at x = 0
- g is differentiable and g' is continuous
g is differentiable while f is not
- g is differentiable but g' is not continuous
Both f and g are differentiable
Q. Let a, bϵR and f:R→R be defined by f(x)=acos(|x3−x|)+b|x|sin(|x3+x|).
Then f is
Then f is
- Differentiable at x=0 if a =0 and b=1
- Differentiable at x=1 if a =1 and b=0
- Differentiable at x=0 if a =1 b=0
- Differentiable at x=1 if a =1 b=1
Q. Let f(x + y) = f(x)f(y) and f(x) = 1 + sin(3x)g(x) where g(x) is continuous then f'(x) is
[Kerala (Engg.) 2005]
[Kerala (Engg.) 2005]
- f(x)g(0)
- 3g(0)
- f(x)cos 3x
- 3 f(x)g(x)
- 3 f(x) g(0)
Q. If f(x) = {sinxx≠nπ, n=0, ±1, ±2...2, otherwise and g(x) = ⎧⎪⎨⎪⎩x2+1, x≠0, 24, x=05, x=2, then limx→0g{f(x)} is
Q. Let f(x + y) = f(x)f(y) and f(x) = 1 + sin(3x)g(x) where g(x) is continuous then f'(x) is
[Kerala (Engg.) 2005]
[Kerala (Engg.) 2005]
- f(x)cos 3x
- 3 f(x) g(0)
- 3 f(x)g(x)
- f(x)g(0)
- 3g(0)
Q. Let f(x+y)=f(x)+f(y) and f(x)=x2g(x) for all x, yϵR, where g(x) is continuous function. Then f′(x) is equal to
- g(0)
- g(0) + g'(x)
- 0
- g'(x)
Q. Let g(x) = x.f(x), where f(x) = f(x)={x sin1x, x≠00, x=0. at x = 0
- g is differentiable but g' is not continuous
g is differentiable while f is not
Both f and g are differentiable
- g is differentiable and g' is continuous
Q. Let a, bϵR and f:R→R be defined by f(x)=acos(|x3−x|)+b|x|sin(|x3+x|).
Then f is
Then f is
- Differentiable at x=0 if a =0 and b=1
- Differentiable at x=1 if a =1 and b=0
- Differentiable at x=0 if a =1 b=0
- Differentiable at x=1 if a =1 b=1
Q. Let f(x) be continuous on [0, 4], differentiable on (0, 4).f(0)=4 and f(4)=−2. If g(x)=f(x)x+2. then the value of g′(c) for some lagrange's constant c∈(0, 4) is
- 12
- 512
- −512
- −712
