The technique options are

1.multiply by a conjugate

2.simplify a complex fraction

3. direct substitution

4. factor and cancel

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a) Lim_(x rarr3)(sqrt(3x+16)-5)/(x-3)multiply by Conjugate{:[sqrt(3x+16)+5],[Lim_(x rarr3)((sqrt(3x+16)-5)(sqrt(3x+16)+5))/((x-3)(sqrt(3x+16)+5))]:}{:[lim_(x rarr3)(3x+16-25)/((x-3)(sqrt(3x+16)+5))],[lim_(x rarr3)(3x-9)/((x-3)(sqrt(3x+16)+5))],[lim_(x rarr3)(3(x-3))/((x-3)(sqrt(3x+16)+5))],[lim_(x rarr3)(3)/(sqrt(3x+16)+5)]:}Apply limits{:[=(3)/(sqrt(3xx3+16)+5)],[=(3)/(sqrt25+5)],[=(3)/(5+5)],[=(3)/(10)]:}The technique used is multiply by Corjugateb) Lim_(h rarr0)((1)/(7+h)-(1)/(7))/(h)Simplify a Complex fractionlim_(h rarr0)((7-(7+h))/(7(7+h)))/(h)lim_(h rarr0)((-h)/(7(7+h)))/(h)Lim_(h rarr0)(-h)/(7h(7+h))lim_(h rarr0)(-1)/(7(7+h))Apply Limit{:[=(-1)/(7(7+0))],[=(-1)/(49)]:}The technique used issimplify a Complex fraction.c ... See the full answer