Limits and Derivatives Online Objective Test | Limits and Derivatives Online Objective Test

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q1.

\underset{x \to 0}{L t} (\frac{\sin x - x}{x}) \cos (\frac{1}{x})

is equal to

A. 1/2

B. -1

C. 1

D. 0

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q2.

\underset{x \to 0}{L t} (\frac{\sin x - x}{x^{4}}) \sin x

equal to

A. 1/6

B. -1/6

C. -1/3

D. 1/3

Answer : Option B
Explaination / Solution:

$\underset{x \to 0}{L t} (\frac{\sin x - x}{x^{3}}) . (\frac{\sin x}{x}) = \underset{x \to 0}{L t} (\frac{\sin x - x}{x^{3}})$

Now using L'Hospital we have, $\frac{\cos x - 1}{3 x^{2}}$

Again using L'Hospital, $\frac{- \sin x}{6 x}$

Again using L'hospital; $\frac{- 1}{6}$

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q3. Let

f (x) = \frac{2 - {(256 - 7 x)}^{1 / 8}}{{(5 x + 32)}^{1 / 5} - 2}, x \neq 0,

then for f to be continuous at x = 0, f (0) must be equal to

A. -1

B. -7/64

C. 7/64

D. 1

Answer : Option C
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q4. If(x)=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪sin[x][x]0,,[x]≠0,thenLtx→0f(x)[x]=0

A. does not exist

B. is equal to 1

C. is equal to 0

D. is equal to -1

Answer : Option A
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q5.

\underset{x \to \infty}{L t} x (a^{1 / x} - 1)

, where a > 0, is equal to

A. logae

B. 1

C. e

D. logea

Answer : Option D
Explaination / Solution:

letx=1t;⇒Ltt→0at−1t=lna

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q6.

\underset{x \to \infty}{L t} \frac{{Σ r}_{r = 1}^{n}}{n^{2}}

is equal to

A. 1/3

B. 1/4

C. 1/2

D. 1

Answer : Option C
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q7.

\underset{n \to \infty}{L t} \frac{Σ_{r = 1}^{n} r^{2}}{n^{3}}

is equal to

A. 0

B. 1/3

C. 1/2

D. 1/4

Answer : Option B
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q8. Ltx→01x

A. does not exist

B. is equal to 0

C. tends to - ∞

D. tends to ∞

Answer : Option A
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q9.

\underset{x \to 0}{L t} x [x]

is equal to

A. 1/2

B. 1 or -1

C. 2

D. 0

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q10.

\underset{x \to 0}{L t} \frac{{(1 + x)}^{n} - 1}{x}

is equal to

A. n2

B. n

C. n - 1

D. 1

Answer : Option B
Explaination / Solution:

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