Home
Class 12
MATHS
Evaluate xlim(xto2) (x-2)/(log(a)(x-1))....

Evaluate x`lim_(xto2) (x-2)/(log_(a)(x-1)).`

Text Solution

AI Generated Solution

To evaluate the limit \( \lim_{x \to 2} \frac{x-2}{\log_a(x-1)} \), we can follow these steps: ### Step 1: Rewrite the logarithm We can rewrite the logarithm in the denominator using the change of base formula: \[ \log_a(x-1) = \frac{\log_e(x-1)}{\log_e(a)} \] Thus, the limit becomes: ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Evaluate lim_(xto2) sin(e^(x-2)-1)/(log(x-1))

Evaluate lim_(xto2^(+)) ([x-2])/(log(x-2)), where [.] represents the greatest integer function.

Evaluate lim_(xto a)(log{1+(x-a)})/((x-a))

Evaluate lim_(xto1) (x^(2)+xlog_(e)x-log_(e)x-1)/((x^(2))-1)

Evaluate Lim_(xto 2) (x^(5)-32)/(x^(2)-4)

Evaluate lim_(xto2) (x^(2)-5x+6)/(x^(2)-4).

Evaluate lim_(xto3) ((x^(2)-9))/((x-3))

Evaluate lim_(xto0) (1-cos2x)/x^(2)

Evaluate: lim_(xto0)(log(1-3x))/(5^(x)-1)

Evaluate lim_(xto2) (x^(2)-x-2)/(x^(2)-2x-sin(x-2)).