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Evaluate : lim(x->pi/4)(1-cot^3x)/(2-cot...

Evaluate : `lim_(x->pi/4)(1-cot^3x)/(2-cotx-cot^3x)`

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`underset(xto pi//4)lim(1-cot^(3)x)/(2-cotx-cot^(3)x)`
`=underset(xto(pi)/(4))lim((1-cotx))/((1-cotx))((1+cotx+cot^(2)x))/((cot^(2)x+cotx+2))`
`=(1+1+1)/(2+1+1)=3/4`
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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
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  3. Evaluate : lim(x->pi/4)(1-cot^3x)/(2-cotx-cot^3x)

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  4. lim(y->0)((x+y)sec(x+y)-xsecx)/y is equal to (a) secx(xtanx+1) (b) x...

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  5. Evaluate lim(x->0)(sqrt(2+x)-sqrt(2))/x

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  6. The value of lim(m->oo)(cos(x/m))^("m") is 1 (b) e (c) e^(-1) (...

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  7. Find the value of underset(xto0)lim(sinx+log(e)(sqrt(1+sin^(2)x)-sinx)...

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  11. Evaluate underset(xto2)lim(sqrt((x+7))-3sqrt((2x-3)))/(root(3)((x+6))-...

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  13. Evaluate: lim(x->oo)(sqrt(3x^2-1)-sqrt(2x^2-1))/(4x+3)

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  14. lim(x->0)(x^4(cot^4x-cot^2x+1)/(tan^4x-tan^2x+1)) is equal to (a) 1 (...

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  15. Evaluate underset(ntooo)limsin^(n)((2pin)/(3n+1)),ninN.

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  16. lim(x->oo)(1/e-x/(1+x))^x is equal to (a) e/(1-e) (b) 0 (c) e/(e^...

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  17. Evaluate underset(xto1)lim(sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrtx))+sqr...

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  18. lim(x->1)(1-x^2)/(sin2pix) is equal to (a)1/(2pi) (b) -1/pi (...

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  19. Evaluate lim(x->2)(x^(10)-1024)/(x^5-32)

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  20. ("lim")(xto0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equals to (a)1 (b) 0 ...

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