Maharashtra State BoardHSC Science (General) 11th
Advertisement Remove all ads

Evaluate the following : limx→2[logx-log2x-2] - Mathematics and Statistics

Sum

Evaluate the following :

`lim_(x -> 2) [(logx - log2)/(x - 2)]`

Advertisement Remove all ads

Solution

Put x = 2 + h. Then x – 2 = h and as x → 2, h → 0.

∴ `lim_(x -> 2) [(log x - log 2)/(x - 2)]`

= `lim_("h" -> 0) [(log(2 + "h") - log2)/"h"]`

= `lim_("h" -> 0) (log ((2 + "h")/2))/"h"`

= `lim_("h" -> 0) (log(1 + "h"/2))/("h"/2) xx 2`

= `1/2 lim_("h" -> 0) (log(1 + "h"/2))/(("h"/2))`

= `1/2 xx 1   ...[because "h" -> 0, "h"/2 -> 0  "and" lim_(x -> 0) (log(1 + x))/x = 1]`

= `1/2`

  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 7 Limits
Miscellaneous Exercise 7 | Q II. (12) | Page 159
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×