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For the curve sqrt(x)+sqrt(y)=1 , (dy)/(...

For the curve `sqrt(x)+sqrt(y)=1` , `(dy)/(dx)` at `(1//4,\ 1//4)` is `1//2` (b) 1 (c) -1 (d) 2

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The correct Answer is:
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`:' f(x) = |cosx-sinx|`,
`:. f'(pi/3) = (sqrt(3) + 1)/(2)`
We know that, `(pi)/(4) lt x lt (pi)/(2).sinx gt cosx`
`:. cosx - sin x le 0` i.e., `f'(x) = -(cosx- sinx)`
`f'(x) = -[-sinx- cosx]`
`:. f'(pi/3) = (-sqrt(3)/2-1/2)= ((sqrt(3)+1)/(2))`
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. Derivative of x^(2) w.r.t. x^(3) is

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  2. If f(x) = |cosx|, then f'(pi/4) is equal to "……."

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  3. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is 1//2 (...

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  4. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

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  5. If f is continuous on its domain D; then |f| is also continuous on D

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  6. If f is continuous on its domain D; then |f| is also continuous on D

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  7. The composition of two continuous function is a continuous function.

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  8. Trigonometric and inverse trigonometric functions are differentiable ...

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  9. If f.g is continuous at x = 0 , then f and g are separately continuou...

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  10. Examine contnuity of the function f(x) = x^(3) + 2x^(2)- 1 at x = 1.

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  11. f(x)={{:(3x+5, if x ge 2),(x^(3), if x le 2):}at x = 2

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  12. f(x)={{:((1-cos2x)/(x^(2)),if x ne 0),(5, if x = 0):} at x = 0.

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  13. f(x) = {{:((2x^(2)-3x-2)/(x-2), if x ne 2), (5, if x = 2):} at x = 2.

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  14. f(x)= {{:((|x-4|)/(2(x-4)), if x ne 4),(0,if x = 4):} at x = 4.

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  15. f(x)={{:(|x|cos\ 1/x, if x ne 0),(0, if x =0):} at x = 0 .

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  16. f(x) = {{:(|x|sin\ (1)/(x-a),if x ne 0),(0, if x =a):} at x = a

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  17. f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x = 0):} at x = 0

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  18. {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if l lt x le 2):} at x = ...

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  19. f(x) = |x| + |x-1| at x = 1.

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  20. f(x)={{:(3x-8, if x le 5),(2k, if x gt 5) :} at x = 5

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