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If f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0)...

If `f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0),(e^x sinx + pi x + lambda In4, x le 0):}` is continuous at x = 0, then the value of `e^lambda` must be

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f(x)={(((1-sin^3x))/(3cos^2x), x lt pi/2), (a, x=pi/2), ((b(1-sinx)...

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  2. Given, f(x)={((x^4-256)/(x-4), x ne 4), ( lambda, x = 4):}. If f is co...

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  3. If f(x)={((8^x-4^x-2^x+1^x)/x^2, x gt 0),(e^x sinx + pi x + lambda In4...

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  4. If f(x)={(((exp{(x+3)ln27})^(1/27[x])-9)/(3^x-27), x lt 3), (lamda.((1...

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  5. If f(x)={(5+x^2, x lt 1), (x-4, x ge 1):} is jump discontinuous, then ...

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  6. A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for...

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  7. If f(x) is continuous and f(9/2) = 2/9, then find lim(xrarr0)9f((1-cos...

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  8. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

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  9. Let f(x) = x + cos x + 2 and g(x) be the inverse function of f(x), the...

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  10. Number of point of discontinuity of f(x)=tan^2x-sec^2x in (0, 2pi) is

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  11. Evaluate the following limits : lim(xrarr0)(5^x-4^x)/(3^x-1)

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  12. Evaluate the following limits : lim(nrarrinfty)(1^2+2^2+3^2+...+n^2)/...

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  13. Evaluate the following limits : lim(xrarrpi/2)(sec x-tan x)

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  14. Evaluate the following limits : lim(xrarrinfty)(x-sqrt(x^2+ x))

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  15. Evaluate the following limits : lim(xrarr0)sqrt((1/2(1-cos2x))/x

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  16. Evaluate the following limits : lim(xrarr0)(1+|sinx|)^(1/x)

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  17. Evaluate the following limits : lim(xrarr1)(1-x)tan frac(pix)2

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  18. Evaluate the following limits : lim(xrarrinfty)x(e^(1/x)-1)

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  19. Evaluate the following limits : lim(xrarrpi/3)sin(pi/3-x)/(2cosx-1)

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  20. Evaluate the following limits : lim(nrarrinfty)n(x^(1/n)-1), xgt0

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