Circle \"True\" at each statement that is always true, and circle \"False\" at e

Question

Circle "True" at each statement that is always true, and circle "False" at each statement is not always true. (a) All functions have antiderivatives. (b) If a function F is an antiderivative of f an {a, b}, then integral^b_a f(x) dx = F(b) - F(a) (c) lim_x rightarrow 0 x^2 - 2x + 4x/3x^2 - x + 8 = 1/3. (d) If f is continuous and positive on [a, b], then integral^b_a (f(x))^2 dx = (integral^b_a f(x)dx)^2 (e) The linearization of f(x) = Squarerootx + 3 = 1 is L(x) = 7/4 + x/4. (f) If F'(x) = G'(x) for all real numbers x, then F(x) = G(x) + C for some constant C. (g) Suppose f(x) is continuous on [-a,a], If f is odd, then integral^a_b f(x) dz = 0. (h) If f'(x_0) = 0, then f(x_0) is either local maximum or local minimum of f(x) (i) The Mean value Theorem states that for any function f(x) defined on [a, b] there is c in [a, b] such that f'(c) = f(b) - f(a)/b - a. (j) The average value of the function f(x) = cos x on the interval[1,3] is 1/2(sin 3 - sin 1).

Explanation / Answer

a) false

B)true

C)false value is 1/2

D)false

E) true

F)true

G) true

H) false because sometimes saddle point occurs

I)true

j) true

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