Advertisement Remove all ads

# Find f(a), if f is continuous at x = a where, f(x) = 1-cos[7(x-π)]5(x-π)2, for x ≠ π at a = π - Mathematics and Statistics

Sum

Find f(a), if f is continuous at x = a where,

f(x) = (1 - cos[7(x - pi)])/(5(x - pi)^2, for x ≠ π at a = π

Advertisement Remove all ads

#### Solution

f is continuous at x = π

∴ f(π) = lim_(x -> pi) "f"(x) =  lim_(x -> pi) (1 - cos[7 (x - pi)])/(5(x - pi)^2

Put x – π = h, as x → π, h → 0

∴ f(π) = lim_("h" -> 0) (1 - cos7"h")/(5"h"^2)

= lim_("h" -> 0) (2sin^2((7"h")/2))/(5"h"^2)

= 2/5 lim_("h" -> 0) (sin^2 ((7"h")/2))/(((7"h")/2)^2) xx (7/2)^2

= 2/5 |lim_("h" -> 0) (sin ((7"h")/2))/(((7"h")/2))|^2 xx 49/4

= 2/5 xx (1)^2 xx 49/4  ...[because lim_(theta -> 0) sintheta/theta = 1]

∴ f(π) = 49/10

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 8 Continuity
Miscellaneous Exercise 8 | Q VII. (2) | Page 178
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?