Given,h(x)= (x-1)²= x²+1-2x
g(x)=3x+5
(h+g)(x)= x²+1-2x+3x+5= x²+x+6.
(h+g)(-2)=(-2)²+(-2)+6=4-2+6=8.
The answer of (h+g)(-2) is 8.
Given that f(x) = 3x + 1 g(x) = 5x - 8 and h(x) = 2x – 1 3 Find:- i) f(-4) = ii) g[h(5)] = iii) f[g(3)] = iv) g[h(x)] = vi) h-1(7) =
TUTI) 8. and h(x) = 3x - 2, a) If g(x) = 2x + 10 3 Find: - (3 marks) and express in its simplest form g[h(x)] = find f'(x) b) If f(x) = = 2x - 1 3x + 4 (4 marks)
Given the functons: f(x)=x² – 3x 8(x) = 13x h(x)=5x+3 Evaluate the function (h )(x) for x= 2. Write your answer in exact simplified form. Select "Undefined" If applicable. (h of)(2) is
3) (15 pts) Given h(x) = -5x2 + 3x + 2, find the equation of the tangent line at x = -2. (Hint: For the tangent line at x = a, find f(a), and f'(a).)
Question 1. (15 pts) Given f(x, y) = 3x 2 + y 3 . (a) Find the gradient of f. (b) Find the directional derivative of f at P0 = (3, 2) in the direction of u = (5/13)i + (12/13)j. Question 1. (15 pts) Given f(L,y) = 3x2 +y?. (a) Find the gradient of f. (b) Find the directional derivative off at P =(3,2) in the direction of u=(5/13)i + (12/13)j.
1 2) (15 pts) Given g(x) g(x+h)-g(x) use the formula g'(x) = lim 6x+3' h0 h to find g'(x). 3) (15 pts) Given h(x) = -3x2 + 5x + 2, find the equation of the tangent line at x = -2. (Hint: For the tangent line at x = a, find f(a), and f'(a).)
Question 32 Find (fg)(x). f(x)= 3x g(x)= 5x+ 7 O None of these og)(x)= x/15+21x O [g)(x)= 15x2 + 7 o Vg)(x)= V8x+ 7 O V&)x)15x2+ 21x og)(x)=xV15+/21x Question 41 1 pts List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). Q(x)=x*- 4x- 5x+8 O 1.8 - 1. - 2. - 4.-8 Ot1.18 None of the above O 1.2.4,8 O +1.2+4,18
Determine g(x +a)-gx) for the following function. 8(x) 32 -3x -1
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
A3.1. Given a function (g(x)=\begin{cases} \dfrac{3x^2+4x-4}{3x-2}, { x \neq \dfrac{2} {3} \\ \\ \dfrac{8}{3}, & x = \dfrac{2}{3} \end{cases} V). Check whether it is continuous at \( x = \dfrac{2}{3} V) and justify your answer with necessary steps.