7. Find the limit or show that it does not exist. t+3 lim -√√2²-1 8. Find the derivative of the function using the defin

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7. Find the limit or show that it does not exist. t+3 lim -√√2²-1 8. Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. (5) f(x) = 4 + 8x - 5x² (10)

9. Find the first and second derivatives of the function. f(x) = 3x - 5x³/5 10. Differentiate the function using the product or quotient rules. a) f(x)= (3x² - 5x)e* b) f(x) = =+e²

11. For what value of x does the graph of f(x) = e* -5x have a horizontal tangent? 12. Differentiate trigonometric functions. a) f(0) = e(cot0 - 0) 1+ secw b) f(w)= 1-secw (10)

13. Find the limit. sine lim 8-00+tano 14. Find an equation of the tangent line to the given curve at the specified point. (5) 1 + x (0.2) 1+ e* f(x) =

15. Find the derivative of the function using the Chain rule. 8 a) f(u) = (u³ u³+1 b) f(x) = sin(+₁)