Limit homework check

I kinda get this but want to make sure my answers are right

59. Suppose limit x->c f(x)=5 and limx->c g(x)=2. Find

a. lim x->c f(x)g(x) b. lim x->c 2f(x)g(x)

for my answers I got 10 for a and 20 for b

60. Suppose lim x->4 f(x)=0 and lim x->4 g(x)=3. Find

a. lim x->4 (g(x)+3) b. lim x->4 xf(x)

c. lim x->4 g^2(x) d. lim x->4 g(x)/f(x)-1

I got 6 for a, 0 for b, 9 for c and -3 for d

61. Suppose lim x->b f(x)=7 and lim x->b g(x)=-3. Find

a. lim x->b (f(x)+g(x)) b. lim ->b f(x) * g(x)

c. lim x->b 4g(x) d. lim x->b f(x)/g(x)

I got 4 for a, -21 for b, -12 for c and -7/3 for d

62. Suppose lim x->-2 p(x)=4, lim x->-2 r(x)=0, and lim x->-2 s(x)=-3. Find

a. lim x->-2 (p(x)+r(x)+s(x)) b. lim x->-2 p(x)*r(x)*s(x)

i got 1 for a and 0 for b

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also 45. let f(x)={a-x^2 if x<2

x^2+5x-3 if x is greater than or equal to 2

For what values of a does lim x->-2 f(x) exist

i got 15 but im not sure if thats right