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If f(x)= {:(mx^(2)+n, x lt 0),(nx +m,0le...

If f(x)= `{:(mx^(2)+n, x lt 0),(nx +m,0le x le 1),(nx^(3) +m, x gt 1):}` For what integers m and n does both `underset(x rarr 0)lim f(x)` and `underset(x rarr 1)lim f(x)` exist

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If f(x)={(mx^2+n, x 1):} . For what integers m and n does both lim_(x rarr 0)f(x) and lim_(x rarr 1)f(x) exist?

lim_(x rarr 0) (|x|)/x is :

MODERN PUBLICATION-LIMITS AND DERIVATIVES-EXERCISE
  1. Find underset(xrarr0)lim f(x), where f(x)={(|x|/x, xne0),(0, x=0):}

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  2. Let f(x)= {(|x|+1,",", x<0),(0,",", x=0),(|x|-1,",", x>0.):} For what...

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  3. If f(x)= {:(mx^(2)+n, x lt 0),(nx +m,0le x le 1),(nx^(3) +m, x gt 1):}...

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  4. Evaluate the following : lim(x rarr 0)(cos x)/(pi-x) .

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  5. Evaluate the following : lim(theta rarr 0)(1-cos theta)/(2 theta^2)...

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  6. Evaluate the following : lim(x rarr 0)(1-cos 4x)/(x^2) .

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  7. Evaluate the following : lim(x rarr 0)(1-cos 4x)/(x^2) .

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  8. Evaluate the following : lim(x rarr 0)(1-cos 2x)/(3x^2) .

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  9. Evaluate the following : lim(theta rarr 0)(1-cos 4 theta)/(1-cos 6 ...

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

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

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

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

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

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

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

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

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

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

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

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