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If f(x)={(x-|x|)/x ,x!=0, 2,x=0, show th...

If `f(x)={(x-|x|)/x ,x!=0, 2,x=0`, show that `lim_(xrarr0)` `f(x)` does not exist.

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
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  2. Evaluate: lim(x->oo) (x+7sinx)/(-2x+13) using sandwich theorem.

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  3. If f(x)={(x-|x|)/x ,x!=0, 2,x=0, show that lim(xrarr0) f(x) does not e...

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  4. The reciprocal of the value of: ("lim")(nvecoo)(1-1/(2^2))(1-1/(3^2))(...

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  5. Show that ("lim")(xrarr0) (e^(1/x)-1)/(e^(1/x)+1) does not exist

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  6. If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,...

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  7. Evaluate : ("lim")(xrarr2^+) ([x-2])/("log"(x-2)) , where [.] repres...

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  8. The value of the limit ("lim")(xvec0)(a^(sqrt(x))-a^(1sqrt(x)))/(a^(sq...

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  9. Evaluate: ("lim")(xrarr0) (sin[cosx])/(1+[cosx])([dot] denotes the g...

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  10. lim(x->0)((1^x+2^x+...........+n^x)/n)^(1/x) is equal to

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  11. Consider the following graph of the function y=f(x)dot Which of the fo...

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  12. If lim(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must b...

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  13. If ("lim")(x->a)[f(x)+g(x)]=2a n d ("lim")(x->a)[f(x)-g(x)]=1, then f...

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  14. Among (i) underset(xtooo)limsec^(-1)((x)/(sinx))" and "(ii) underset(x...

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  15. Evaluate "lim"(x->0)(3x+|x|)/(7x-5|x|)

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  16. The value of lim(x->0)(1+sinx-cosx+"log"(1-x))/(x^3) is 1/2 (b) -...

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  17. lim(xvecoo)(e^(1/x^2)-1)/(2tan^-1(x^2)-pi) is equal to (a) 1 (b) -...

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  18. Evaluate: lim(x->oo) (1+1/(a+bx))^(c+dx) , where a,b,c and dare positi...

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  19. If x1=3 and x(n+1)=sqrt(2+xn),ngeq1,t h e n""("lim")(xrarroo)xn is (...

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  20. Evaluate: ("lim")(xrarroo)(1+1/x)^x

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