Consider the following graph of the function y=f(x). Which of the following is//are correct? `(a) lim_(xto1) f(x)` does not exist. `(b) lim_(xto2)f(x)` does not exist. `(c) lim_(xto3) f(x)=3.` `(d)lim_(xto1.99) f(x)`exists.

Consider the following graph of the function y=f(x). Which of the foll

1.	Consider the following graph of the function y=f(x). Which of the following is//are correct? `(a) lim_(xto1) f(x)` does not exist. `(b) lim_(xto2)f(x)` does not exist. `(c) lim_(xto3) f(x)=3.` `(d)lim_(xto1.99) f(x)`exists.
Answer» Correct Answer - (a), ( c ), (d) `a. underset(xto1^(+))limf(x)=3" and "underset(xto1^(-))limf(x)=2." Thus,"underset(xto1)limf(x)` does not exist. `b. underset(xto2^(+))limf(x)=underset(xto2^(-))limf(x)=3." Thus,"underset(xto2)limf(x)` exist. `c. underset(xto3^(+))limf(x)=underset(xto3^(-))limf(x)=3." Thus,"underset(xto3)limf(x)` exist. `d. underset(xto1.99^(+))limf(x)=underset(xto1.99^(-))limf(x)=3." Thus,"underset(xto1.99)limf(x)` exist.

`lim_(xto oo) (1)/(n) {1+e^(1//n)+e^(2//n)+e^(3//n)+.....+e^((n-1)/(n))}` is equal toA. eB. `-e`C. `e-1`D. `1-e`
`lim_(xto oo) ((nsqrt(a)+nsqrt(b))/(2))^n,a,b,gt 0` equalsA. 1B. `sqrt(pq)`C. `pq`D. `(pq)/(2)`
If `lim_(xto oo){(x^2+1)/(x+1)-(ax+b)}to oo`, thenA. `a in (1,oo)`B. `a ne 1 , b in R`C. `a in (-oo,1)`D. none of these
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\(f\left(x\right)=\left[\left(\frac{min\left(t^2+4t+6\right)\sin \left(x\right)}{x}\right)\right]\)where [.] represents greatest integer function, then find \(\lim _{x\to 0}\left(f\left(x\right)\right)\)
`lim_(xrarr0) ((1-cos2x)^2)/(2xtanx-xtan2x)` , isA. 2B. `-(1)/(2)`C. `(1)/(2)`D. `-2`
The value of `lim_(xrarroo) ((x+3)/(x-1))^(x+1)` isA. eB. `e^2`C. `e^4`D. `1//e`
`lim_(xrarroo) ((x+2)/(x+1))^(x+3)` is equal toA. 1B. eC. `e^2`D. `e^3`
`lim_(x->0)((1-cos2x)sin5x)/(x^2sin3x)`A. `(10)/(3)`B. `(3)/(10)`C. `(6)/(5)`D. `(5)/(6)`
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