A) Find the Domain of the following functions 1) f(x) = vx – 3+ V5 – x 2) f(x) = 3 – log2 x² – (log2 x)² 3) f(x) = Vx2 –1+ v1- x² - - - |

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: 3. If ƒ(x) = log₂(−(x − 6)) and g(x) = √(x + ²) a) Determine the domain of g(x) + f(x) b) Is there a…

A: We want to find domain of g+f

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is %3D Log(-12). O 2i -12 None of them O…

A: We have to find Derivative using definition and L'Hospital Rule.

Q: #1 If F(x) = 2 log x and G(x) = x 2 + 3, find G[F(x)]. 2log(x² + 3) (2logx)² + 3 2(x² + 3)logx

A:

Q: When comparing the f(x) = x² + 2x and g(x) = log(2x + 1), on which interval are both functions…

A: Sol:- fx=x2+2x< 0⇒xx+2<0Find the signs of the factors of xx+2 x2+2x<0  :  Solution:…

Q: B. Find the domain of each function. 1. f(x)=1+x 2. f(x) =1-V 3. h(x) = x-4 4. F(x) = x-1 5. G(x) =…

A:

Q: 2. Find the domain. (a) f(x) = log2(log3 x) (b) g(x) = log [In(x – 1)] (c) h(x) = In [log(x – 1)]…

A: Domain.

Q: 4. 1. Let f(x) = (sinx)*tan(1 – x)e30x. Find the maximum of f(x) in [0,1] and ɛ = 0.05. (by handly…

A: Given: fx=sinx6tan1-xe30x. We have to find the maximum of fx in 0,1.

Q: Find all the critical points and local maximums and minimums of each function. f(x) = 5x+cos(2x+1)

A:

Q: Alog f(x) = log[1+ Af(x), f(x)

A: We have to solve given problem:

Q: 11. Find the domain of f(x). a. f(x) = /42-7x. b. f(x) = log3(x - 38) %3D

A: domain= all the values of x for which function exists.

Q: - 22. Find f'(x) if f(x)= log2 x*- 5 x4- 8 a. f'(x)= (x* – 5)In(2) x*- 5 b. f'(x)= x*-8 12x3 c.…

A: First convert base of log then differentiate

Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: c) If f'(x) =3+ 4x and the curve f(x) passes through the point (1, 8) i) Find f(x) ii) Find the…

A:

Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: Employ the concept of growth of functions to compute the smallest intege for which the function f(x)…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Answer

Q: Consider a function f with domain {x|x # 0} and the following derivatives: f'(x) = bx-1 and f"(x) =…

A:

Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

A:

Q: 4. 1. Let f (x) = (sinx)ʻtan(1 – x)e30x. Find the maximum of f(x) in [0,1] and & = 0.05. (by handly…

A: We will use Newton's method of optimization to find the maximum value of f(x)

Q: 3. Find the implied domain for the following functions: (a) f(x) = Vx² – x – 6. %3D log, (x – 2) |…

A:

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: f(x)=3x+3-18 and f-1(x)=log3(x+18)-3 Show that (f•f-1)(x)=x

A:

Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

Q: For the function f(x)=5.log (x* - 10x +x+30)-5, on the interval (-4, 4), approximate the local…

A:

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x>0

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + i is O Undefined. O Log(-6). O None of them O…

A:

Q: Consider a function f with domain {x|x + 0} and the following derivatives: 2 bx3 bx² – 1 bx? f' (x)…

A:

Q: 1. Differentiate. Show your work to get credit. а) f(x) = log10 vx by using the chain rule. %3D…

A: RECALL:( Chain Rule differentiation)       If f and g both are differentiable function and F(x) is a…

Q: 2 Compute the derivative f'(x) of the logistic sigmoi 1 f (x) : 1+ exp(-x)

A: We have to find

Q: For which value(s) of k, if any, is the function 1 (²) = x [kx² - log₂ (x) 2xk²x + 5 continuous on…

A: Use continuity definition of function

Q: Given the functions f(x) = log₂ (2x) and g(x) = 2x - 3, which of the following statements is true?…

A: Here, the given functions are f(x)=log2(2x) =ln (2x)ln 2(used change of base)& g(x)=2x-3 Here,…

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

A:

Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

A:

Q: 3. f(x) = log2 (x+7)-1 X Domain: Range: End Behavior: As x→→ f(x)→∞ As x→→_____ f(x)→→x x-intercept:…

A: Given:- f(x)=log3(x+7)-1 To find:- Domain,Range ,end behaviour,x and y intercept

Q: 1. Find the derivative of the following (a) f(x) = log-(r* +2) + 7** (b) k(r) = In(x) + 5e¯ (c) j(z)…

A:

Q: Based on a study, the Lorenz curves for the distribution of incomes for bankers and actuaries are…

A: Given: Lorenz curve for the distribution of incomes for bankers, fx=110x+910x3. Lorenz curve for…

Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: Consider the function g defined by 1 g(x, y) = cos (7x/) - CoS log3(x – y)

A: Given problem:-

Q: Suppose the functions f, g and h are defined by 33 f(x) = 3* + and g(x) = log̟ x + log̟ (x + 6) + 4…

A: In this question, we find the domain of each of the given function f(x), g(x) and h(x). In other…

Q: Find the least integer n such that f(x) is O(x") for the function 3x +x log ax

A: This is a problem of finite math, and complexity.

Q: Find the minimum of the function f(x) = (X/log X) by using the quadratic-interpolation method with…

A: Find the minimum of the function f(x) = (X/log X) by using the quadratic-interpolation method with…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x>0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: The given functions are: fx=2x2-1x2+3x2+1 and gx=x2+872-3x25 The person's brother believes that,…

Q: Definite integrals Evaluate the following definite integrals. Use Theorem 7.7 to express your answer…

A: Evaluate: ∫-22dtt2-9