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Let f(x)= {(cosx,if, xge0),(x+k,if, x<0....

Let `f(x)= {(cosx,if, xge0),(x+k,if, x<0.):}` Find the value of the constant k, given that `lim_(x rarr 0) f(x)` exists.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Evaluate the following limit : lim(t rarr 1)(1-1/t)/(sin[pi(t-1)]) ...

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  2. Evaluate the following limit : lim(x rarr pi/2)(pi/2-x)tanx .

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  3. Let f(x)= {(cosx,if, xge0),(x+k,if, x<0.):} Find the value of the con...

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  4. Evaluate the following limit : lim(x rarr 0)e^x .

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  5. Evaluate the following limit : lim(x rarr -oo)e^x .

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  6. Evaluate the following limit : lim(x rarr oo)e^-x .

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  7. Evaluate the following limit : lim(x rarr -oo)2^x .

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  8. Evaluate the following limit : lim(x rarr 0) (e^(4x)-1)/x .

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  9. Evaluate the following limit : lim(x rarr 0) (e^(3x)-1)/x .

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  10. Evaluate the following limit : lim(x rarr 0) (2^x-1)/x .

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  11. Evaluate the following limit : lim(x rarr 0) (3^(2+x)-9)/x .

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  12. Evaluate the following limit : lim(x rarr 0) (e^(2+x)-e^2)/x .

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  13. Evaluate the following limit : lim(x rarr 0) (e^x-x-1)/x.

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  14. Evaluate the following limit : lim(x rarr 0) (e^x-sinx-1)/x .

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  15. Evaluate the following limit : lim(x rarr 0) (e^(3+x)-sinx-e^3)/x .

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  16. Evaluate the following limit : lim(x rarr 0) (e^x-e^(sinx))/(x-sinx)...

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  17. Evaluate the following limit : lim(x rarr 5) (e^x-e^5)/(x-5) .

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  18. Evaluate the following limit : lim(x rarr 2) (e^x-e^2)/(x-2) .

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  19. Evaluate the following limit : lim(x rarr 3) (e^x-e^3)/(x-3) .

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  20. Evaluate the following limit : lim(x rarr 0)(a^x-b^x)/x (a>0, b>0) .

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