What is the limit as x approaches a+of (cos(x)ln(x-a))/(ln(e^x-e^a)) ?

The limit as x approaches a+of (cos(x)ln(x-a))/(ln(e^x-e^a)) is cos(a)

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limit as x approaches a+of (cos(x)ln(x-a))/(ln(e^x-e^a))

x \to a + lim (\frac{cos ( x ) ln ( x - a )}{ln ( e ^{x} - e ^{a} )})

cos (a)

Solution steps

x \to a + lim (\frac{cos ( x ) ln ( x - a )}{ln ( e ^{x} - e ^{a} )})

Plug in the value

x = a

= \frac{cos ( a ) ln ( a - a )}{ln ( e ^{a} - e ^{a} )}

Simplify

\frac{cos ( a ) ln ( a - a )}{ln ( e ^{a} - e ^{a} )} : cos (a)

= cos (a)

What is the limit as x approaches a+of (cos(x)ln(x-a))/(ln(e^x-e^a)) ?
The limit as x approaches a+of (cos(x)ln(x-a))/(ln(e^x-e^a)) is cos(a)