Решение
1) limx-->0 [(√(7 - x) - √(7 + x))*(√(7 - x) + √(7 + x))] / (√7 *x) =
= lim x-->0  [(√(7 - x)² - (√(7 + x))²] / (√7 * x) = 
 limx-->0 (7 - x - 7 - x) /(√7 * x) =  lim x-->0 (- 2x) / (√7 * x) =
 = -2 / √7 = - 2√7 / 7
2)  lim x-->-1 [(√5+ x) - 2)*(√(5 + x) + 2)*√(8 - x) + 3)] /
 /[(√(8 - x) - 3)*(√(8 - x) + 3)*(√(5 + x) + 2)] = lim x-->-1 [(5 + x - 4)*
* √(8- x) + 3)] / [(8 - x - 9) * (√(5 + x) + 2)] 
=   lim x-->-1 [(1 + x)*(√(8 - x) + 3)] / [(11 -x)*(√(5 + x) + 2)] = 0
3)    lim x-->4 [(2 - √x)*(2 + √x)*(√(6x + 1) + 5) ] / [(6x+ 1) - 5)* 
* (√(6x + 1) + 5)* (2 + √x)] =   lim x-->4 [(4 - x)*(√(6x + 1) +5) ] /
/ [(6x + 1 - 25)* (2 + √x)] = lim x-->4 [(4 - x)*(√(6x + 1) +5)] /
/ [6*(x - 4)* (2 + √x) = - lim x-->4 [(4 - x)*(√(6x + 1) + 5)] /
  [6*(4 - x)* (2 + √x)] =  - lim x-->4 [(√(6x + 1) + 5)] /  [6* (2 + √x)] = 10/24 =
= 5 /12
4)  lim x--> -1 [√(x + 20) - 4)*(√(x + 20) + 4)] / (x³+ 64) = 
 lim x--> - 1 (x + 20 - 16) / (x³+ 64) = lim x--> - 1 (x + 4) / [(x+ 4)*(x² - 4x + 16)] = lim x--> -1  [1 / (x² - 4x + 16)] = 1/21
5)  lim x--> 3 (2x³- 3x - 9) / [(√x - 2) - √(4 - x)] = 
2x² - 3x - 9 = 0
D = 9 + 4*2*9 = 81
x = (3 - 9)/4 = - 3/2
x = (3 + 9)/4 = 3
 lim x--> 3 [2*(x + 1,5)*(x - 3)*(√(x - 2) + √(4 - x)] /
 / [(√(x - 2) - √(4 - x)) * (√(x - 2) + √(4 - x))] =  
lim x--> 3 [2*(x + 1,5)*(x - 3)*(√(x - 2) + √(4 - x))] / (x - 2 - 4 + x) =
= lim x--> 3 [2*(x + 1,5)*(x - 3)*(√(x - 2) + √(4 - x))] / [2*(x - 3)] =
= lim x--> 3 [2*(x + 1,5)*(√(x - 2) + √(4 - x))] / 2 =
= (2*4,5*2) / 2 = 9