f,g are tow real function and a ER such that 3 an open interval {a} C D, A Dg and let lim-af(x) and limx¬a 9(x) are exist x) = L, and limx¬a g(x) = L2 then %3D (x).g(x)) exist and lim,a(f(x). g(x)) = L1. L2 %3D ),9(x) # 0exist and lima () =,L2 # 0 %3D L2 (x) ,n E Z*,f(x) 2 0 if n even exist lima Vf(x) = "/L1, %3D ven

Q: х+4 a) Compute lim X3 (x-5)(x-3)

A:

Q: How does the function behave as lim x → 3- for 7/(3(x-3)(5-x))?

A:

Q: →0 (2a−3/2a+ 5)^(2a+1) should i use lhopital or direct substitute the value of

A:

Q: CONSIDER THE FOLLOWING FUNCTIONS. f22x+1 AiD gca)= xー1 a) DE TERMINE jG&) =f(x)• g(x) Lim…

A:

Q: a+5 If f(z) = 3z-5 and g(z) = 3 %3D (a) f(g(z)) = (b) g(f(z)) = %3D (c) Thus g(z) is called an…

A:

Q: e*+1 Differentiate the function f(x)= In -3x +1 -3e A) 4e** +1 +1 3e B) e +1 +1 3e C) 3x 1. D) E) +1

A: Topic: differentiation

Q: Let f and g be functions defined by, f(x) = Vx+ 2 and g(x) = Vx2 + 1. Find the functions gof, , f +…

A:

Q: The limit of the function lim (-1)Inxis x-0 a b C d 1 11

A:

Q: Suppose that f(x)=(x+2)(x-2)^2. (G) Use interval notation to indicate where f(x) is concave down.…

A:

Q: Find the maximum of f(x) = -x4 - 2*x3 - 8*x2 -5*x in the range of [-2, 1]

A:

Q: Consider these 2 functions f(x) = fex ifxco 1+/6x² if x>0 g(x) = e¯* In (f(x) −2) What is the domain…

A: The functions are

Q: The graph of function f(x) = x³ 6x2 + 9x + 1 is concave upward on (-∞, 2) (-0, 0) (2, оо) о (-2, 2)

A: f is concave up when f''(x) is greater than 0

Q: Which of the following functions showing lim f (x) = f(c)? 1+4x f(x) = 1+ 3x; c = 2 f(x) = ;c = 0…

A: We have to check

Q: 5. If f(x) = 2 x + 3 a) f-¹(g(x)) and g(x) = 21, find b) the domain and range of f-¹(g(x))

A:

Q: Two functions are defined as follows: f(x)=7-2x² and g(x)=x²+4 (a) Use ANY graphing tool to…

A: Here We have to find the point of intersection of the two curves.

Q: b) Let f(x) = x²-1 2-1 ' √x-1 0 < x < 1 1<x<3 2-1 ' 5x+3, 3x Find lim, 1 f(x). 3x-7 c) Let f(x) =…

A: The b part of the question can be solved using the concept of limits.The c part of the question can…

Q: Ex x-2 XE3, X-2 12) Consider メレ3 2) lim. (f(x) b) lim. (f(x)

A: Topic:- limit

Q: Suppose the point (-3, 10) lies on y = f(x) and the point (2, -3) lie point on the function y =…

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: .3 2x -3x lim Зx3 +4 Typ (Туp

A:

Q: (g) lim (x- Vx +x - Vx-x (h) lim 3x²

A:

Q: S 3x + 2 x² + 3x – 1 I-2 |

A: Given that: f(x)=3x+2            x&lt;-2x2+3x-1   x≥-2

Q: 4) Find fog, gof , f+g and fg where f (x) = x^2 + 1 and g(x) = x + 2, are functions from R to R

A:

Q: 6. Let f(x) = x − 1 and g(x) = (x + 2)², find the following: a) Domain of f(x) b) Range of f(x) c)…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: The composite function denoted by feg is defined by O af = g(x) = f(g(x) O b. f - g(x) = f(x) •g{x)…

A:

Q: Sketch the graph of f if a = 2. (a) f(r) = a² (b) f(x) = -a (c) f(x) = 3a* (d) fx) = a**3 (e) f(x) =…

A: Hey, Thanks for the question. Since you have posted multiple subparts, as per our guidelines we will…

Q: 5. Find limf(x) x4-3 a) f(x) = 5x4 %3D 6x4 - 3 b) f(x) = 3x3 2x3 - 9 c) f(x) = %3D 3x5

A: We have to find limx→∞fx for a fx=x4-35x4b fx=6x4-33x3c fx=2x3-93x5 Since all above limit has ∞∞…

Q: 7. lim (x2 + 1)i – x

A: