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Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(...

Let `f(x)={x+1,x >0, 2-x ,xlt=0` and `g(x)={x+3,x<1,x^2-2x-2,1lt=x<2, x-5,xgeq2` Find the LHL and RHL of `g(f(x))` at `x=0` and, hence, find `lim_(x->0)g(f(x)).`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
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  2. Evaluate: [("lim")(xrarr0)(tan^(-1)x)/x], where [.]represent the g...

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  3. Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x<1,x^2-2x-2,1lt=x<2, ...

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  4. Evaluate: ("lim")(xto pi/4)(sqrt(2)cosx-1)/(cotx-1)

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  5. underset(xto0)lim[(1-e^(x))(sinx)/(|x|)] is (where [.] represents the ...

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  6. Evaluate: lim(x->0)(1-cosm x)/(1-cosn x)

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  7. underset(xtooo)lim(cot^(-1)(x^(-a)log(a)x))/(sec^(-1)(a^(x)log(x)a)),(...

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  8. Evaluate: lim(x->0)(tan2x-x)/(3x-sinx)

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  9. The value of ("lim")(x->a)sqrt(a^2-x^2)cot(pi/2sqrt((a-x)/(a+x))) is (...

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  10. Evaluate: lim(x->0)(cot2x-cos e c2x)/x

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  11. lim(x->0)(log(1+x+x^2)+"log"(1-x+x^2))/(secx-cosx)=

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  12. Evaluate: lim(n->oo)ncos(pi/(4n))sin(pi/(4n))

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  13. The value of lim(n->oo)[(2n)/(2n^2-1)cos((n+1)/(2n-1))-n/(1-2n)dot(n(-...

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  14. Evaluate: ("lim")(h->0)(2[sqrt(3)sin(pi/6+h)-cos(pi/6+h)])/(sqrt(3)h(s...

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  15. Evaluate: lim(x->0)8/(x^8){1-cos((x^2)/2)-cos((x^2)/4)+cos((x^2)/2)cos...

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  16. Evaluate: lim(x->0)(cos^(-1)((1-x^2)/(1+x^2)))/(sin^(-1)x)

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  17. Evaluate: lim(n->oo)n^2{sqrt((1-cos(1/n))sqrt((1-cos(1/n)) sqrt((1-cos...

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  18. Evaluate: ("lim")(x→0,y→0)(y^2+sinx)/(x^2+siny^2) where (x , y)→(0,0)...

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  19. Evaluate underset(ntooo)lim{cos((x)/(2))cos((x)/(4))cos((x)/(8))...cos...

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  20. Find the value of alpha so that lim(x->0)1/(x^2)(e^(alphax)-e^x-x)=3/...

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