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Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
Concept: undefined >> undefined
If y = tan(x + y), find `("d"y)/("d"x)`
Concept: undefined >> undefined
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If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Concept: undefined >> undefined
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Concept: undefined >> undefined
Let f(x)= |cosx|. Then, ______.
Concept: undefined >> undefined
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
Concept: undefined >> undefined
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
Concept: undefined >> undefined
| 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 |
Concept: undefined >> undefined
|sinx| is a differentiable function for every value of x.
Concept: undefined >> undefined
cos |x| is differentiable everywhere.
Concept: undefined >> undefined
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
Concept: undefined >> undefined
`sin sqrt(x) + cos^2 sqrt(x)`
Concept: undefined >> undefined
sinn (ax2 + bx + c)
Concept: undefined >> undefined
`cos(tan sqrt(x + 1))`
Concept: undefined >> undefined
sinx2 + sin2x + sin2(x2)
Concept: undefined >> undefined
`sin^-1 1/sqrt(x + 1)`
Concept: undefined >> undefined
(sin x)cosx
Concept: undefined >> undefined
sinmx . cosnx
Concept: undefined >> undefined
(x + 1)2(x + 2)3(x + 3)4
Concept: undefined >> undefined
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
Concept: undefined >> undefined
