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If f.g is continuous at x = 0 , then f ...

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

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Let `f(x) = sinx` and `g(x) = cotx`
`:. f(x). g(x) = sinx. (cosx)/(sinx) = cosx`
which is continuous at `x = 0` but `cot x` is not continuous at `x = 0`.
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
  1. The composition of two continuous function is a continuous function.

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

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

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

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

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

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

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

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

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

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

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  12. {{:(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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  13. f(x) = |x| + |x-1| at x = 1.

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

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  15. If f(x)={(2^(x+2)-16)/(4^x-16),ifx!=2k ,ifx=2i scon t inuou sa tx=2,f...

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  16. f(x) = {{:((sqrt(1+kx)-sqrt(1-kx))/(x),if -1 le x lt 0),((2x+1)/(x-1),...

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  17. f(x) = {{:((1-coskx)/(x sinx), if x ne 0),(1/2, if x = 0):} at x = 0

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  18. Prove that the function f defined by f(x) = {{:((x)/(|x|+2x^(2)), if ...

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  19. Find the values of a and b sucht that the function f defined by ...

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  20. If the function f(x) = 1/(x+2), then find the points of discountinu...

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