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Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/...

Evaluate : `lim_(x to 0) {tan(pi/4+x)}^(1/x)`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not gr...

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  2. Use formula lim(x->0)(a^x-1)/x=log(a) to find lim(x->0)(2^x-1)/((1+x)^...

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  3. Evaluate : lim(x to 0) {tan(pi/4+x)}^(1/x)

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  4. f(x) is the integral of (2sinx-sin2x)/(x^3),x!=0. Find lim(x->0)f^...

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  5. Evaluate underset (h to 0) lim ((a+h)^(2) sin (a+h) -a^(2) sin a)/h .

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  6. underset(xtooo)lim(x(logx)^(3))/(1+x+x^(2)) equals

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  7. underset(xto0)lim((2^(m)+x)^(1//m)-(2^(n)+x)^(1//n))/(x) is equal to

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  8. lim(x to 1) (1-x)tan((pix)/2)

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  9. If f(x)={sinx ,x!=npi,n in I2,ot h e r w i s e g(x)={x^2+1,x!=0,4,x=...

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  10. ("lim")(xvec0)[min(y^2-4y+11)(sinx)/x](w h e r e[dot]d e not e st h e ...

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  11. lim(x to pi/2)sin(xcosx)/("cos"(xsinx)) is equal to (a) 0 (b) pi/2 ...

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  12. If lim xto0(x^(-3)sin3x+a x^(-2)+b) exists and is equal to 0, then (a)...

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  13. If lim(xto0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  14. lim(xto1) ((1-x)(1-x^(2))...(1-x^(2n)))/({(1-x)(1-x^(2))...(1-x^(n))}^...

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  15. The value of lim(x->0)([(100 x)/(sinx)]+[(99sinx)/x]) (where [.] repre...

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  16. The value of lim(x->1/(sqrt(2))) ((x-"cos" (sin^(-1)x))/ (1-tan(sin^(-...

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  17. The value of underset(xtooo)lim((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((...

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  18. Let lim(xto0) ([x]^(2))/(x^(2))=m, where [.] denotes greatest integer....

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  19. underset(xto1)lim(xsin(x-[x]))/(x-1), where [.] denotes the greatest i...

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  20. underset(xto0)lim[(sin(sgn(x)))/((sgn(x)))], where [.] denotes the gre...

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