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Examine the continuity of the function f...

Examine the continuity of the function `f(x)= {(1+x",","if " x le 2),(5-x",","if" x gt 2):}` at x= 2

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x=2
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. Examine the differentiability of f, where f is defined by f(x) = {(x...

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  2. Determine if f defined by f(x) = {(x^(2)"sin" (1)/(x)",","if" x ne 0),...

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  3. Examine the continuity of the function f(x)= {(1+x",","if " x le 2),(5...

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  4. Show that f(x) = |x-5| is continuous but not differentiable at x= 5

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  5. A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for ...

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  6. Differentiate 2^(cos^(2)x)

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  7. Differentiate (8^(x))/(x^(8))

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  8. Differentiate log (x + sqrt(x^(2) + a))

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  9. Differentiate the following with respect to x: log [log (log x^(5))]

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  10. Differentiate sin sqrtx + cos^(2) sqrtx

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  11. Differentiate sin^(n) (a x^(2) + bx + c)

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  12. Differentiate cos (tan sqrt(x+ 1))

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  13. Differentiate sin x^(2) + sin^(2)x + sin^(2) (x^(2))

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  14. Differentiate sin^(-1) ((1)/(sqrt(x + 1)))

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  15. Differentiate (sin x)^(cos x)

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  16. Differentiate sin^(m) x.cos^(n) x

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  17. Differentiate (x+1)^(2) (x + 2)^(3) (x + 3)^(4)

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  18. Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (...

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  19. Differentiate tan^(-1) sqrt((1-cos x)/(1 + cos x)), - (pi)/(4) lt x lt...

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  20. Differentiate tan^(-1) (sec x + tan x), -(pi)/(2) lt x lt (pi)/(2)

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