Quantitative Aptitude - Limits and Continuity
Exam Duration: 45 Mins Total Questions : 30
Left hand limit of (limit 5x when x tends to 0) is -
- (a)
1/5
- (b)
-5
- (c)
5
- (d)
0
\(\underset{x\to 0}{lim} { \frac { \sqrt { 1+2{ x }^{ 2 } } -\sqrt { 1-2{ x }^{ 2 } } }{ { x }^{ 2 } } } \)is equal to -
- (a)
2
- (b)
-2
- (c)
1/2
- (d)
None of these
\(\underset{x\to 0}{lim} { \left( \frac { { e }^{ 2x }-1 }{ x } \right) } \)
- (a)
1/2
- (b)
2
- (c)
0
- (d)
None of these
\(\underset { x\rightarrow 0 }{ lim } \frac { log(1+px) }{ { e }^{ 3x }-1 } \) is equal to -
- (a)
p/3
- (b)
p
- (c)
1/3
- (d)
None of these
Evaluate \(\frac { lim }{ x\rightarrow 0 } \frac { { 9 }^{ x }-{ 3 }^{ x } }{ { 4 }^{ x }-{ 2 }^{ x } } \)
- (a)
\(\frac{log3}{log2}\)
- (b)
\(\frac{log4}{log2}\)
- (c)
\(\frac{log9}{log2}\)
- (d)
\(\frac{log3}{log4}\)
The value \(\underset { X\rightarrow 0 }{ lim } \frac { { u }^{ x }+{ v }^{ x }+{ w }^{ x }-3 }{ x } \) of is -
- (a)
uvw
- (b)
log uvw
- (c)
log\(\frac{1}{uvw}\)
- (d)
None of these
\(\underset { X\rightarrow 1 }{ lim } \frac { { x }^{ 3 }-{ 5x }^{ 2 }+2x+2 }{ { x }^{ 3 }+2{ x }^{ 2 }-6x+3 } \) is equal to -
- (a)
5
- (b)
-5
- (c)
1/5
- (d)
None of these
\(\underset { x\rightarrow 1 }{ lim } { loge }^{ x }\) is evaluated to be -
- (a)
0
- (b)
e
- (c)
1
- (d)
None of these
Evaluate \(\underset { x\rightarrow 2 }{ lim } \frac { { x }^{ 2 }+2x-1 }{ \sqrt { { x }^{ 2 }+2 } } \)
- (a)
\(\frac{1}{\sqrt2}\)
- (b)
\(\frac{3}{\sqrt2}\)
- (c)
\(\frac{7}{\sqrt6}\)
- (d)
\(\frac{1}{4}\)
Evaluate \(\underset { x\rightarrow 5 }{ lim } \frac { 1 }{ x-1 } \)
- (a)
1
- (b)
0
- (c)
1/2
- (d)
1/4
Limit \(\frac{1}{x+5}\) when x tends to 5 -
- (a)
exists
- (b)
does not exist
- (c)
zero
- (d)
∞
\(\underset { x\rightarrow 3 }{ lim } \frac { { x }^{ 2 }-5x+6 }{ { x }-3 } \) is equal to -
- (a)
-1
- (b)
+∞
- (c)
1
- (d)
Does not exist
Evaluate \(\underset { x\rightarrow 3 }{ lim } \frac { { x }^{ 2 }+4x+3 }{ { x }^{ 2 }+6x+9 } \)
- (a)
1
- (b)
2/3
- (c)
0
- (d)
1/3
\(\underset { x\rightarrow -2 }{ lim } \frac { { x }^{ 2 }-{ 4 } }{ x+2 } \)
- (a)
4
- (b)
-4
- (c)
does not exist
- (d)
None of these
If f(x)=\(\frac { { x }^{ 3 }+{ a }^{ 3 } }{ x+a } \) for x≠- a = K for x = - a. Is continuous at X = - a then the value of K is
- (a)
-3a2
- (b)
-2a2
- (c)
3a2
- (d)
2a2
Evaluate \(\underset { x\rightarrow 9 }{ lim } \frac { \sqrt { x } -3 }{ x-9 } \)
- (a)
\(\frac{1}{3}\)
- (b)
\(\frac{1}{6}\)
- (c)
1
- (d)
3
Compute the value of \(\underset { x\rightarrow 1 }{ lim } \left( \frac { { x }^{ 2 }+3x+2 }{ { x }^{ 3 }+{ 2x }^{ 2 }-x+1 } \right) \)
- (a)
5
- (b)
9
- (c)
7
- (d)
2
\(\underset { x\rightarrow 1 }{ lim } \frac { { x }^{ 2 }-\sqrt { x } }{ \sqrt { x } -1 } \) is equal to -
- (a)
-3
- (b)
-1/3
- (c)
3
- (d)
None of these
Lt (0.7 + 0.07 + 0.007 + ..... n terms) =
- (a)
\(\frac{77}{98}\)
- (b)
\(\frac{9}{7}\)
- (c)
\(\frac{7}{9}\)
- (d)
\(\frac{99}{77}\)
Evaluate \(\underset { x\rightarrow \infty }{ lim } \left( 1+\frac { 9 }{ x } \right) ^{ x }\)
- (a)
e9
- (b)
9
- (c)
1
- (d)
e1
\(\underset { x\rightarrow \infty }{ lim } \frac { 3x+5 }{ { x }^{ 3 }+12 } \) is equaI to -
- (a)
0
- (b)
1
- (c)
-1
- (d)
Does not exist
The value of the limit when n tends to infinity of the expression \(\frac { { 3 }n^{ 3 }+{ 7n }^{ 2 }-11n+19 }{ { 17n }^{ 4 }+{ 18n }^{ 3 }-20n+45 } \) is -
- (a)
0
- (b)
1
- (c)
-1
- (d)
1\(\sqrt2\)
Find \(\underset { n\rightarrow \infty }{ lim } \left( \frac { 1 }{ 1-{ n }^{ 2 } } +\frac { 2 }{ 1-{ n }^{ 2 } } +\frac { 3 }{ 1-{ n }^{ 2 } } .....+\frac { n }{ 1-{ n }^{ 2 } } \right) \)
- (a)
1/3
- (b)
0
- (c)
-1/2
- (d)
-1/4
Find \(\underset { n\rightarrow \infty }{ lim } { n }^{ n }{ (1+n) }^{ -n }\)
- (a)
e-1
- (b)
e
- (c)
1
- (d)
-1
Find \(\lim _{ n\rightarrow \infty }{ \frac { \{ 1.3.5...(2n-1)\} { (n+1) }^{ 4 } }{ { n }^{ 4 }\{ 1.3.5...(2n-1)(2n+1)\} } } \)
- (a)
5
- (b)
e-1
- (c)
0
- (d)
none
variable is known to be______________ if it can assume any value from a given interval
- (a)
Discrete
- (b)
Continuous
- (c)
Attribute
- (d)
Characteristic
If f(x) = 5x, when x > 0 = -5x, when x < 0 Then f(x) is -
- (a)
Discontinuous at x = 0
- (b)
Discontinuous for all x
- (c)
Continuous at x = 0
- (d)
None of these
A function f(x) is defined in (0,3) as follows f(x) = X2 when 0<x<1 = x when 1≤ x<2 = (1/4) x3 when 2≤x<3 now f(x) is continuous at -
- (a)
x = 1
- (b)
x = 3
- (c)
x = 0
- (d)
None of these
If f(x) = 5+3x for x ≥0 and f(x) = 5-3x for x<0 then f(x) is-
- (a)
Continuous at x = 0
- (b)
Discontinuous and defined at x = 0
- (c)
Discontinuous and undefined at x = 0
- (d)
None of these
A function f(x) defined as follows f(x) = x + 1 when x s 1 = 3 - px when x > 1 The value of p for which f(x) is continuous at x = 1 is:
- (a)
-1
- (b)
1
- (c)
0
- (d)
none of these
