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### Limit and Continuity

19. $\underset{x\to \mathrm{\infty }}{lim}\frac{x\left(x+1\right)}{{x}^{2}}=$ [2075]

1

0

2

20. $\underset{x\to \frac{\pi }{4}}{lim}\frac{se{c}^{2}x-2}{tanx-1}=$ [2075]

0

1

2

-2

19. $\underset{x\to \infty }{lim}\frac{3{x}^{2}+2x-5}{6{x}^{2}+4x-7}=$ = [2074]

2

3

5/7

1/2

20. $\underset{x\to 0}{lim}\frac{1-coxax}{{x}^{2}}=$ [2074]

a2/2

a2

2a2

4a2

18. $\underset{x\to \infty }{lim}\frac{1+2+...+n}{{n}^{2}}=$ [2073]

1/2

0

1/n

n

19. $\underset{x\to \infty }{lim}\frac{5{x}^{2}+4xtanx}{{x}^{2}}=$ = [2073]

9

0

5

4

19. $\underset{x\to 0}{lim}\frac{x-2}{\sqrt{{x}^{2}-4}}$ [2072]

0/0

0

1

4

20. $\underset{x\to 0}{lim}\frac{1-2co{s}^{2}ax}{{x}^{2}}$ [2072]

0

a2

2a2

2

18. The value of $\underset{x\to 2}{lim}\frac{{x}^{5}-{2}^{5}}{x-2}=$ is [2071]

80

40

10

0

19. The value of $\underset{x\to 0}{lim}\frac{3x+4tan2x}{x}$ is [2071]

7

3

11

4

6. $\underset{x\to \mathrm{0}}{lim}\frac{{a}^{x}-{b}^{x}}{x}$ is equal to [2070]

0

log(ab)

log(a/b)

log(b/a)

24. If $\underset{x\to 0}{lim}f\left(x\right)\ne \underset{x\to 0}{lim}f\left(x\right)$ then f(x) is said to be an [2070]

Infinite discontinuity

Removal Discontinuity

Jump Discontinuity

None

### Other Questions

$\underset{x\to 3}{lim}\frac{{x}^{2}-9}{x-3}$

3

6

0

None Of These

$\underset{x\to 0}{lim}\frac{{2}^{x}-{3}^{x}-2}{x}$

loge2.loge3

loge5

loge6

None of These

$\underset{x\to 0}{lim}\frac{\left(1+x{\right)}^{n}-1}{x}$

1

n

n-1

nn-1

$\underset{x\to 0}{lim}\frac{\sqrt{1+2{x}^{2}}-\sqrt{1-2{x}^{2}}}{{x}^{2}}$

2

4

0

None of these

$\underset{x\to 0}{lim}\left(1+3x{\right)}^{\frac{1}{x}}$

1/e

3

e

e3

$\underset{x\to \mathrm{\infty }}{lim}\frac{si{n}^{2}2x}{{x}^{2}}$

4

-4

sinx

cosx

$\underset{x\to \mathrm{2}}{lim}\frac{{x}^{2}-4}{x-2}$

2

4

6

8

$\underset{x\to 5}{lim}\frac{x-5}{{x}^{2}-25}$

$-\frac{1}{10}$

$-\frac{1}{5}$

$\frac{1}{5}$

$\frac{1}{10}$

$\underset{x\to 3}{lim}\frac{{x}^{2}-7x+12}{x-3}$

0

1

-1

2

$\underset{x\to 2}{lim}{x}^{2}+5x+1$

15

1

9

6

$\underset{x\to 1}{lim}\frac{{x}^{2}-3x+2}{x-1}$

1

0

-1

2

$\underset{x\to 1}{lim}\frac{{x}^{2}+x-20}{x-4}$

8

-20

-15

9

$\underset{x\to 0}{lim}\frac{\left(x+4{\right)}^{2}-16}{x}$

4

5

6

8

$\underset{x\to 0}{lim}\frac{\sqrt{{x}^{3}}}{\sqrt{x}}$

0

1

2

3

$\underset{x\to \mathrm{\infty }}{lim}\frac{3}{1+{t}^{2}}$

0

1

2

3

$\underset{x\to \mathrm{\infty }}{lim}\frac{{x}^{2}+x+1}{\left(3x+2{\right)}^{2}}$

1

1/3

0

1/9

$\underset{x\to \mathrm{\infty }}{lim}\frac{2{x}^{2}}{\left(x+2{\right)}^{3}}$

0

1

2

3

$\underset{x\to 0}{lim}\frac{1+sinx}{1+cosx}$

1

1/2

3

Do not exist

$\underset{x\to \mathrm{\infty }}{lim}\left(\frac{3x-4}{3x+2}{\right)}^{\frac{x+1}{3}}$

e-1

e-2

e-(1/2)

e-(2/3)

$\underset{x\to \mathrm{0}}{lim}\frac{sin{x}^{°}}{x}$

1

π

π/180

None of these

$\underset{x\to 0}{lim}\frac{1-\mathrm{cos2x}}{x}$

0

1

2

4

$\underset{x\to 0}{lim}\frac{xcosx-sinx}{{x}^{2}sinx}$

1/2

-(1/2)

1/3

-(1/3)

$\underset{x\to \mathrm{\infty }}{lim}\frac{sinx}{x}$

0

1

does not exist

I there is