3.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS
Calculus
- If find f x( )=1 x1 x+− , [Ans.^12 ]
- If f(x) = x + | x | are f(2) and f(– 2) equal? [Ans. no]
- Evaluate : (i)
2
x 1
limx 1
→ x 1
+
+ (ii)
2
x 1
limx 1
→ x 1
−
− (iii) x^2
lim x 2
→ x 2
−
− [Ans. (i) 1 (ii) 2 (ii) no exisstance]
- Evaluate : (i)
2
x 1
lim x 5x 6
→ x 1
+ −
− (ii)
x
x 0
lime 1
→ x
− [Ans. (i) 7 (ii) 1]
- Evaluate :
2
x 1^2
limx 4x 3
→ − x 7x 8
+ +
− − [Ans.
2
9
− ]
- Find the value of xlim→ 0 1 1 x− x− [Ans.^12 ]
- If f(x) = x^2 , evaluate : limh→ 0 f x h f x( + h)− ( ) [Ans. 2x]
- Is the function f(x) = | x | continuous at x = 0 [Ans. Yes]
- Evaluate :
2
x^2
lim 6 5x.
→∞ 4x 15x
−
+ [Ans.
1
2 ]
- A functions is defined as follows :
f(x) = 2x – 1, x < 3
= k, x = 3
= 8 – x, x > 3.
For what value of k, f(x) is continuous at x = 3? [Ans. 2] - A function is defined as follows :
f(x) = 1, x > 0
= 0, x = 0
= - 1 x < 0. Is the function is continuous at x = 0 [Ans. no]