4. Determine when the following pairs of functions are linearly independent. (a) yı(t) = erit; y(t) = er²t, r₁,72 € R (b) y(t) = cos(at); 32(t) = sin(at), a = R (c) y₁ (t) = cosh(at); y₂(t) = sinh(at), a € R

2. Consider the function f (x) = r° – x² - 5x +13. (a) Compute f'(x). (b) Find the slope of the tangent line to the graph of f at the point (2, 7). (c) Find an equation of the tangent line to the graph of f at the point (2, 7). (d) Find the value(s) of x at which the tangent line to f is horizontal (i,.e., f' (x) = 0). (You'll need to remember how to factor a quadratic here.)

Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) = x² , g(x) = 4|x|2 NO ANSWER * 2. f(1) = ed"cos(Ht) = ed'sin(ut) ,u # 0 NO ANSWER 3. f(0) = cos(30) g(6) = 2 cos (8) – 2 cos(8) %3D NO ANSWER + 4. f(t) = 3t g(t) = |t|

3. Find F(t) such that F'(t) = sec³(t) tan³ (t) and F = 0.

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#38 Find derivatives of the Functions: A) (Zx-5)-3 and B)