A) If 8^x+1 = 2^2x+7, what is x?
8. Compute the limit arctan 2x lim +- X (a) 0 (b) 7/2 (c) –7/2 (d) e (e) 1
TiMX 2+ 2x-3 X²-2x+1 8 90x = y 25x to continuous at in {+ x +3 forxay x=3? Why 37-5, for 74 continuous atx4 ? why?
Evaluate the function for the given value of x. 1-2x-5, {/x-7). for x<-1 for -1 <x<1 for x21 19, Find f(-1) undefined -8. -3 8.
7. Prove or disprove: If we know that 2X +6=4 (mod 8), then X +3 = 2 (mod 8). 8. Prove or disprove: If we know that 2X+6 = 4 (mod 7), then X+3 = 2 (mod 7). 9. Let S be the set {311, 254, -172,45,2019, 111,3}. Find a subset T such that the sum of the elements in divisible by 7
part b 2. Let f(x) = x + 2x + x + 2x + 1 in Zy[x]. (a) (12 points) Show that f(x) has no roots in Zs. (b) (8 points) If f(x) is not irreducible, what are the degrees of its irreducible factors? Explain. [Do not factor f (2)]
1. Evaluate the expression when x=-5 - 3x² + 2x - 7 2. Simplify: 4+ 2(x + 3) – 7(2x - 5) 3. Subtract: (5y² + 4y + 3) - (y? – 7y + 10)
1. Find Derivative: y=2x^3 ln(2x^3+7) a. y' = 36x^4 ÷ 2x^3+7 b. y'=12x^5 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) c. y' = -36x^4 ÷ 2x^3 +7 d. y'=12x^5 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) e. y'=2x^3 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) f. 2x^3 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) 2. Find exact value of the expression. Sin(arctan(x/4)) a. √16-x^2 ÷ x. b. x ÷√16-x^2. c. undefined. d. √16+x^2 ÷ x. e. 4 ÷ √16-x^2 f.none
2x-x2 8) Simplificar x²-x-2
1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x, 0<x< 2, f(x + 4) = f(x) (a)[3] Sketch the graph of this function over three periods. Examine the convergence at any discontinuities (b)[5] Find the Fourier series of f(x) 2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods...
What is the composition(fog)(x) when f(x) = 2x+6 and g(x)=x2-1, before simplifying? a.(fog)(x)=x2-1+2x+6 b.(fog)(x)=(2x+6)2-1 c.(fog)(x)=2(x2-1)+6 d.(fog)(x)=(2x+6)(x2-1)