Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Continuity sums for practice, Exams of Mathematics

Continuity sums students of high school as well as universities can practice these sums.

Typology: Exams

2020/2021

Uploaded on 05/12/2021

inaya-mirza
inaya-mirza 🇮🇳

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Continuity
1. Draw the graph of the function f(x) and discuss the continuity of the function f(x) .
(i) f(x) = x+2, when x ≥ 1,
= 3x , when x< 1.
(ii) f(x) = x+1 when x ≤ 2
= 2−x when x > 2 .
(iii) f(x) = |𝑥|
𝑥 ,
(iv) f(x) = |𝑥 1|.
2. A function f (x) is defined as f (x) = 5x 1, for x < 1,
= 4x, for x 1.
Discuss the continuity at x = 1.
3. A function f (x) is defined as f (x) = x 2, for x < 3,
= 1 for x = 3,
= 4−x, for x > 3.
Discuss the continuity at x = 3.
4. Discus the continuity of the following functions at the given points:-
(a).
5
25
)( 2
x
x
xf
when x > 5
=10 when x = 5
=
3
153x
when x < 5, at the point x = 5.
(b). f (x) = x2 when x > 2
=5 when x = 2
=2x when x < 2, at the point x=2.
(c). f (x) = 1 + x2 if 0 ≤ x ≤1
=2 x if x > 1 at the point x = 1.
5. A function
)(x
is defined as follows:-
2
)( xx
for x < 1
= 2.5 for x = 1
= x2 + 2 for x > 1
Is
)(x
continuous at x = 1?
6. Discuss the continuity of the function at x = 4.
f(x) = 𝑥216
𝑥−4 , when x ≠ 4,
= 8 , when x= 4.
7. Find the value of k for which the following function is continuous at x=3.
f (x) =
3
9
2
x
x
when x ≠ 3
= k when x = 3.

Partial preview of the text

Download Continuity sums for practice and more Exams Mathematics in PDF only on Docsity!

Continuity

  1. Draw the graph of the function f(x) and discuss the continuity of the function f(x). (i) f(x) = x+2, when x ≥ 1, = 3x , when x< 1. (ii) f(x) = x+1 when x ≤ 2 = 2−x when x > 2. (iii) f(x) = |𝑥| 𝑥 , (iv) f(x) = |𝑥 − 1 |.
  2. A function f (x) is defined as f (x) = 5 x – 1 , for x < 1 , = 4x, for x ≥ 1. Discuss the continuity at x = 1.
  3. A function f (x) is defined as f (x) = x – 2, for x < 3, = 1 for x = 3, = 4−x, for x > 3. Discuss the continuity at x = 3.
  4. Discus the continuity of the following functions at the given points:- (a). 5 ()^225    x (^) f x x when x > 5 =10 when x = 5 = 3 3 x ^15 when x < 5, at the point x = 5. (b). f (x) = x^2 when x > 2 = 5 when x = 2 =2x when x < 2, at the point x=2. (c). f (x) = 1 + x^2 if 0 ≤ x ≤ =2 – x if x > 1 at the point x = 1.
  5. A function ( x )is defined as follows:- ( x )  x^2 for x < 1 = 2.5 for x = 1 = x^2 + 2 for x > 1 Is ( x )continuous at x = 1?
  6. Discuss the continuity of the function at x = 4. f(x) = 𝑥^2 − 16 𝑥− 4 ,^ when^ x ≠ 4, = 8 , when x= 4.
  7. Find the value of k for which the following function is continuous at x=3. f (x) = 3 (^29)   x x when x ≠ 3 = k when x = 3.