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Evaluate the following : lim(xrarr 0)...

Evaluate the following :
`lim_(xrarr 0)(1-cos mx)/(1-cos nx)` , m, n being fixed non-zero real numbers.

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MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Evaluate the following : lim(theta rarr 0)(1-cos 4 theta)/(1-cos 6 ...

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  2. Evaluate the following : lim(x rarr 0)(cos 2x-1)/(cos x-1) .

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  3. Evaluate the following : lim(xrarr 0)(1-cos mx)/(1-cos nx) , m, n b...

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  4. Evaluate the following : lim(xrarr 0)(1-cos 5x)/(1-cos 6x).

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  5. Evaluate the following : lim(theta rarr 0)(1-cos theta)/(1-cos 3 th...

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  6. Evaluate the following : lim(xrarr 0)(1-cos^2 x)/(3 tan^2 x) .

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  7. Evaluate the following : lim(xrarr 0)((1-cos 2x)/(sin^2 2x)) .

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  8. Evaluate the following : lim(xrarr 0)(2 sinx -sin 2x)/x^3 .

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  9. Evaluate the following : lim(xrarr 0)((3 sinx -sin 3x)/x^3) .

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  10. Evaluate the following : lim(x rarr 0)(sinx)/x .

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  11. Evaluate the following : lim(x rarr 0)(sin ax)/(bx) .

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  12. Evaluate the following : lim(x rarr 0)x/(tan x) .

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  13. Evaluate the following : lim(x rarr 0)(sin^2x)/(2x) .

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  14. Evaluate the following : lim(x rarr 0) x^2/(sin x^2) .

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  15. Evaluate the following : lim(x rarr 0)(sin x^2)/x .

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  16. Evaluate the following : lim(x rarr 0)(sin 4x)/(sin 2x) .

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  17. Evaluate the following : lim(x rarr 0)(sin(pi-x))/(pi(pi-x)) .

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  18. Evaluate the following : lim(x rarr 0)(sin 5x)/(tan 3x) .

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  19. Evaluate the following : lim(theta rarr 0)(sin3 theta)/(tan2 theta)...

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  20. Evaluate the following : lim(theta rarr 0)(sin4 theta)/(tan3 theta)...

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