Advertisements
Advertisements
प्रश्न
| COLUMN-I | COLUMN-II |
| (A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(a) |x| |
| (B) Every continuous function is differentiable | (b) True |
| (C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(c) 6 |
| (D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(d) False |
Advertisements
उत्तर
| COLUMN-I | COLUMN-II |
| (A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(c) 6 |
| (B) Every continuous function is differentiable | (d) False |
| (C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(a) |x| |
| (D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(b) True |
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Differentiate the function with respect to x.
`cos (sqrtx)`
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
If y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx = |(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`.
Discuss the continuity and differentiability of the
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
`"If y" = (sec^-1 "x")^2 , "x" > 0 "show that" "x"^2 ("x"^2 - 1) (d^2"y")/(d"x"^2) + (2"x"^3 - "x") (d"y")/(d"x") - 2 = 0`
|sinx| is a differentiable function for every value of x.
cos |x| is differentiable everywhere.
sinn (ax2 + bx + c)
(sin x)cosx
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
A function is said to be continuous for x ∈ R, if ____________.
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
If sin y = x sin (a + y), then value of dy/dx is
If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
Which expression defines the derivative of a real function \[f\] at a point \[c\] in its domain?
If \[u\] and \[v\] are differentiable functions, which formula is correct?
If \[u\] and \[v\] are differentiable functions, what is \[(uv)'\]?
For \[v\ne0\], what is the derivative of \[\frac{u}{v}\]?
What is \[\frac{d}{dx}(\tan x)\]?
Which limit is the left-hand derivative at \[x=c\]?
What is the practical condition for differentiability at a point?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If a function \[f\] is differentiable at a point \[c\], what must be true at that point?
For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?
Why is \[|x|\] not differentiable at \[x=0\]?
When does a derivative exist?
