Question: 7. Using Theorem 7.10 or Theorem 9.30, prove that each of the following limits exists. Find a value for the limit in each case. (a)

7. Using Theorem 7.10 or Theorem 9.30, prove that each of the following limits exists. Find a value for the limit in each case.

(a) lim ln/2 sin x ~k k3 dx.

k--+oo 0 4 - x

(b) lim f1 x2 f (-k/ ) dx,

where f is continuously differentiable on [0,1] and 1'(0) > 0.

(c) 11 (logk + x) lim x3 cos k dx.
k--->oo 0 + X (d)

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