Evaluate the limits of the following questions please show

Question

Evaluate the limits of the following questions. Please show work and use a table if necessary.

1. lim_x→∞ (x²/5) + 7

2. lim_x→∞ (1/x) + 6

3. lim_x→∞ 5x⁶(1/x⁶)

4. lim_x→∞ (x³+3x²-4/x⁵)

5. lim_x→∞ (1/x²) + 6

6. lim_x→∞ (3x²-6x-24/x²-10x+24)

7. lim_x→∞ (x² +10x +24/(2x+2)(x+4))

8. lim_x→∞ (2x!/x!(3x))

9. lim_x→∞ (7•7/7)

10. lim_ψ→0 ψ²/5

Using the limit definition of the derivative find the tangent line to the equation at the given point:

11. f(x) = 2√(3x+4)                       (0, 4)

12. f(x) = 7x2 + 2x + (16/32)         (0, 0.5)

13. f(x) = 3x+2/7x-1                      (0, -2)

14. f(x) = x²                                  (0, 0)

15. f(x) = (7/21)x⁴                         (0, 0)