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Evaluate : lim(x->1)(x^2+x(log)e x-(log)...

Evaluate : `lim_(x->1)(x^2+x(log)_e x-(log)_e x-1)/((x^2-1)`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate : lim(x->1)(2/(1-x^2)+1/(x-1))

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  2. lim(x->0)((1+5x^2)/(1+3x^2))^(1//x^2)=

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  3. Evaluate : lim(x->1)(x^2+x(log)e x-(log)e x-1)/((x^2-1)

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  4. If L= lim(ntooo) (2xx3^(2)xx2^(3)xx3^(4)...xx2^(n-1)xx3^(n))^((1)/((n^...

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  5. Evaluate lim(x->pi/4)(1-sin2x)/(1+cos4x)

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  6. The value of underset(xtooo)lim(log(e)(log(e)x))/(e^(sqrt(x))) is .

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

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

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

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

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

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  12. The value of lim(hto0) (ln(1+2h)-2ln (1+h))/(h^2), is

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  13. Evaluate : lim(x->oo)(a x^2+b x+c)/(dx^2+e x+f)dot

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  14. The value of lim(x->1)(2-x)^(tan((pix)/2)) is (a)e^(-2/pi) (b) e^...

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

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  16. lim(x->0) (sinx^n)/((sinx)^m),(mltn), is equal to (a) 1 (b) 0 (c) n...

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

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

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

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  20. 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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