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2. Evaluate the following limits. (a) lim x→1+ ln(x) /ln(x − 1) (b) limx→2π x sin(x)...

2. Evaluate the following limits.

(a) lim x→1+

ln(x) /ln(x − 1)

(b) limx→2π

x sin(x) + x ^2 − 4π^2/x − 2π

sin^2 (3x)/x^2

Solutions

Expert Solution

(a)

The right limit of ln(x) at 1 is 0.

The right limit of ln(x-1) at 1 is .

Hence,

(b)

By substituting x = 2 in the function, we get the indeterminate form 0/0. Hence, we need to apply the L'Hopital's

rule.

(c)

milcah answered 1 year ago

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