CPT Chapter Limits and Continuity

With Anand.Duration:4hrs25min

What are Limits?
Basic of Limit
Avoid Indeterminant
Infinity Problem
Formula based Problem
Condition for discontinuous
Check Limit Exist or Not
Check Continuous or Not

Avoid Indeterminant-

lim (4x4+5x3+7x2+6x)/(5x5+7x2+x) is equal to
x →0
a) 6 b) 5 c) -6 d) none of these

lim(x2-5x+6)(x2-3x+2)/(x3-3x2+4) is equal to
x →2

a)1/3 b)3 c) -⅓ ) none of these

lim (4-x2)/3-√(x2+5) is equal to
x →2
a) 6 b) 1/6 c) –6 d) none of these

lim (x2-1)/(√3x+1-√5x-1) is evaluated to be
x →1
a) 4 b) ¼ c) -4 d)none of these

Formulae-

f(x) ex-1 = loge = logee =1
x →0 x

f(x) ax-1 = loga = logea
x →0 x

f(x) log(1+x) = loge = 1
x →0 x

f(x) loga(1+x) = logae
x →0 x

f(x) log(1+1/x) = loge = 1
x →∞ 1/x

f(x) (1+1/x )x=e
x →∞

f(x) (1+x )1/x=e
x →∞

Formula based Problem-

lim (e2x-1)/x is equal to
x →0
a)1/2
(b) 2
(c) e5
(d) none of these.

Lim x→0 (2e1/x -3x)/(e1/x +x)=-

a)-3
b)0
c)2
d)4

lim (5x +3x -2)/x will be equal to
x →0
a) loge15 b) log (1/15) c) log e d) none of these

Odd & Even Function-

if f(x) is an odd function then

a){f(-x)+f(x)}/2 is an even function
b){|x|+1} is even when [x] = the integer x≤
c) [f(x)+f(-x)]/2 is neither even or odd
d) none of these

Continuity-

When a function is discontinuous-
A function will be discontinuous when the function is indeterminate.

The points of discontinuity of the function :
f(x) = (2x2+6x-5)/(12x2+x-20) are, when x is

a)-4/5 and 5/3
b)-4/3 and 5/4
c)4/5 and -5/3
d)4/3 and -5/4

Checking Limit Exist or Not-

If f(x)=(x+1)/√(6x2+3)+3x then lim f(x) and f(-1)
x →-1
a) both exists
b) one exists and other does not exist
c) both do not exists
d)none of these

lim y→0 (3y+ |y|)/(7y -5|y|)=
a)2
b)⅙
c)3/7
d)does not exist

Checking Continuity-

A function f(x) is defined 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.

Conclusion-
What are Limits?
Basic of Limit
Avoid Indeterminant
Infinity Problem
Formula based Problem
Condition for discontinuous
Check Limit Exist or Not
Check Continuous or Not

Notes

CPT Exam Exposure

Take Quiz

Differentiation

Sets Functions and Relations

 Show you appreciate by sharing!