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Examine the continuity of the following ...

Examine the continuity of the following function at `x = 2 `:
`f(x) = {{:(3x + 1 "," ,x le 2),(4x - 1",", x gt 2):}`

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The correct Answer is:
Continuous
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BETTER CHOICE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)
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  2. Examine the continuity of the following function at x = 2 : f(x) = {...

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  3. Examine the continuity of the following function at x = 2 : f(x) = {...

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  4. Differentiate the following w.r.t.x y = log(x+4+sqrt(x^2 +8x+4))

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  5. Differentiate the following w.r.t.x y= log(x+2+sqrt(x^2 + 4x+1))

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  6. y = sqrt(cos x + sqrt(cosx + sqrt(cosx + ...."to " oo))) prove that (2...

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  7. y = sqrt(sin x + sqrt(sinx + sqrt(sinx + ....1 oo))) prove that (2y - ...

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  8. y = sqrt(tan x + sqrt(tanx + sqrt(tanx + ...."to" oo))) prove that (2y...

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  9. If sin y = x cos (a + y), prove that (dy)/(dx) = (cos^2 (a + y))/(cos ...

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  10. x = a (theta - sin theta), y = a (1 + cos theta) find dy/dx

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  11. If y = (sin x)^(cos x) find (dy)/(dx).

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  12. If y = (cos x)^(sin x) find (dy)/(dx)

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  13. Differentiate cos^(-1)((1 - x^2)/(1 + x^2)) w.r.t. tan^(-1)x.

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  14. Differentiate sin^(-1)((2x)/(1 + x^2)) w.r.t. tan^(-1) x.

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  15. Differentiate tan^(-1)(2x)/(1 - x^2) w.r.t. tan^(-1) x.

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  16. Differentiate cot^(-1)((sqrt(1 + x^2) - 1)/(x)) w.r.t.x.

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  17. y = [x + sqrt(x^2 + 1)]^p , prove that (x^2 + 1)y2 + xy1 - p^2y = 0

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  18. Verify Rolle's theorem for the following functions f(x) = (x + 2)(x-...

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  19. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-6) i...

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  20. Verify Rolle's theorem for the following functions f(x)=(x-2)(x-4)^2...

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