Question #042d9

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Answer 1 · 2018-02-06T18:32:57

# ln2#.

We will use the following Standard Forms of Limit :

#(1) : lim_(h to 0) (a^h-1)/h=lna, a gt 0#.

# (2) : lim_(theta to 0)sintheta/theta=1#.

Now, the reqd. lim.#=lim_(x to 0)(2^(sinx)-1)/x#,

#=lim_(x to 0)(2^(sinx)-1)/sinx*sinx/x#,

#=lim_(sinx to 0)(2^(sinx)-1)/sinx*lim_(x to 0)sinx/x#,

#=(ln2)(1)#,

#=ln2#.