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Question
`sin sqrt(x) + cos^2 sqrt(x)`
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Solution
Let y = `sin sqrt(x) + cos^2 sqrt(x)`
Differentiating both sides w.r.t. x
`"dy"/"dx" = "d"/"dx" (sin sqrt(x)) + "d"/"dx" (cos^2 sqrt(x))`
= `cos sqrt(x) * "d"/"dx" (sqrt(x)) + 2cossqrt(x)* "d"/"dx" (cos sqrt(x))`
= `cossqrt(x) * 1/(2sqrt(x)) + 2cos sqrt(x) (- sin sqrt(x)) * "d"/"dx" sqrt(x)`
= `1/(2sqrt(x)) * cos sqrt(x) - 2 cos sqrt(x) * sin sqrt(x) * 1/(2sqrt(x))`
= `(cos sqrt(x))/(2sqrt(x)) - (sin 2sqrt(x))/(2sqrt(x))`
Hence, `"dy"/"dx" = (cos sqrt(x))/(2sqrt(x)) - (sin 2sqrt(x))/(2sqrt(x))`.
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| 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| |
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| (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 |
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