Limits of Standard Functions
Limits, Continuity and Differentiability

79567 \(\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}\) is equal to :

1 0
2 1
3 18
4 36
Limits, Continuity and Differentiability

79569 The value of \(\lim _{x \rightarrow \infty} \frac{\sqrt{1+x^{4}}-\left(1+x^{2}\right)}{x^{2}}\) is equal to :

1 0
2 -1
3 2
4 none of these
Limits, Continuity and Differentiability

79570 If \(\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{(x-1)}=5\), then \((a+b)\) is equal to

1 -4
2 -3
3 -7
4 7
Limits, Continuity and Differentiability

79571 \(\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^{2}}=\)

1 -2
2 Limit does not exists
3 Limit exists
4 2
Limits, Continuity and Differentiability

79567 \(\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}\) is equal to :

1 0
2 1
3 18
4 36
Limits, Continuity and Differentiability

79569 The value of \(\lim _{x \rightarrow \infty} \frac{\sqrt{1+x^{4}}-\left(1+x^{2}\right)}{x^{2}}\) is equal to :

1 0
2 -1
3 2
4 none of these
Limits, Continuity and Differentiability

79570 If \(\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{(x-1)}=5\), then \((a+b)\) is equal to

1 -4
2 -3
3 -7
4 7
Limits, Continuity and Differentiability

79571 \(\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^{2}}=\)

1 -2
2 Limit does not exists
3 Limit exists
4 2
Limits, Continuity and Differentiability

79567 \(\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}\) is equal to :

1 0
2 1
3 18
4 36
Limits, Continuity and Differentiability

79569 The value of \(\lim _{x \rightarrow \infty} \frac{\sqrt{1+x^{4}}-\left(1+x^{2}\right)}{x^{2}}\) is equal to :

1 0
2 -1
3 2
4 none of these
Limits, Continuity and Differentiability

79570 If \(\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{(x-1)}=5\), then \((a+b)\) is equal to

1 -4
2 -3
3 -7
4 7
Limits, Continuity and Differentiability

79571 \(\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^{2}}=\)

1 -2
2 Limit does not exists
3 Limit exists
4 2
Limits, Continuity and Differentiability

79567 \(\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}\) is equal to :

1 0
2 1
3 18
4 36
Limits, Continuity and Differentiability

79569 The value of \(\lim _{x \rightarrow \infty} \frac{\sqrt{1+x^{4}}-\left(1+x^{2}\right)}{x^{2}}\) is equal to :

1 0
2 -1
3 2
4 none of these
Limits, Continuity and Differentiability

79570 If \(\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{(x-1)}=5\), then \((a+b)\) is equal to

1 -4
2 -3
3 -7
4 7
Limits, Continuity and Differentiability

79571 \(\lim _{x \rightarrow 0} \frac{2 x}{|x|+x^{2}}=\)

1 -2
2 Limit does not exists
3 Limit exists
4 2