Home
Class 11
MATHS
Evaluate lim(xrarr2)((e^(x)-e^(2))/(x-2)...

Evaluate `lim_(xrarr2)((e^(x)-e^(2))/(x-2)).`

Text Solution

Verified by Experts

Put `(x-2)=y,` so that when `x to2` then `y to0.`
`thereforelim_(xto2)((e^(x)-e^(2))/(x-2))=lim_(yto0)((e^(y+2)-e^(2))/(y))`
`=lim_(yto0){e^(2).((e^(y)-1)/(y))}`
`=e^(2).lim_(yto0)((e^(y)-1)/(y))=(e^(2)xx1)=e^(2)[becauselim_(yto0)((e^(y)-1)/(y))=1].`
Promotional Banner

Topper's Solved these Questions

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27A|40 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27B|72 Videos

  • LIMIT

    RS AGGARWAL|Exercise EXERCISE 27C|15 Videos

  • HYPERBOLA

    RS AGGARWAL|Exercise EXERCISE 24|23 Videos

  • LINEAR INEQUATIONS (IN ONE VARIABLE)

    RS AGGARWAL|Exercise EXERCISE 6B|12 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr2)((e^(x)-e^(2))/(x-2))

Evaluate lim_(xrarr0)((3^(x)-2^(3x))/(x)).

Evalute lim_(xrarr0)((e^(3x)-1)/(x)).

Evaluate: lim_(xrarr2) (x^(3)-2x^(2))/(x^(2)-5x+6)

Evaluate: lim_(xrarr2) (x^(2)-4)/(x-2)

Evaluate lim_(xrarr2){((x^(2)-4))/(sqrt(3x-2)-sqrt(x+2))}.

Evaluate: lim_(x rarr0)(e^(x)+e^(-x)-2)/(x^(2))

Evaluate: lim_(x rarr0)(e^(x)-e^(-x)-2x)/(x^(3))

Evaluate the following limits: lim_(xrarr0)((e^(2+x)-e^(2))/(x))

Evaluate the following limits: lim_(xrarr0)((e^(2+x)-e^(2))/(x))