1. Which of the following is the reverse operation of [f(x)]? dx A) f f(x) dx B) Jdx C)f cdx D) dx 2. If you were asked to evaluate fdx, which of the following would be a good step? A) transform with a negative exponent B) apply the natural logarithm formula C) u-substitution with u = x⁹ D) bring out the constant as

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: Sulphur dioxide is released into the atmosphere when coal is burnt . In a city the amount of sulphur…

A:

Q: Find the inverse function of f. f(x) = Vx2 - 9, STEP 1: Replace f(x) with y. x² -9 2 STEP 2:…

A: f(x) =√(x2-9) , x>=3

Q: a) x1+2log x = 100.x log x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the inverse function of f. f(x) = x6, x ≥ 0

A: A function is a relation between set of input values and the output values. For the given function,…

Q: Use logarithmic differentiation to find the derivative of y y = X X+7 OA. OB. O C. (3)√ 2 7 O D. X…

A: topic- differentiation properties of log used:log(ab)=blog(a)logab=log(a)-log(b)derivative formula…

Q: For each statement, indicate if it is True or False. Assume x and y represent positive values. v…

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: Condense Conden se into a single logarithm. 4) 6log § x – 31og § y 4.

A: Given 6log8x-3log8y

Q: Write a function newt (f, df, x0) which implements Newton's method to identify a root of the…

A:

Q: 7. Find the inverse function for each of the following: (a) y= log, (x+8)-2

A:

Q: Part 1 of (a) For each function given in the table, write an equivalent function using base e. That…

A:

Q: Evaluate log( 3 + j4) 5elT/3 = A + jB, determine the imaginary component B. A 0.057 B 0.781 -1.2343…

A:

Q: Find the loylor seies exponsions around the pont Xo = 1 of the functions given bellow: (Note: By…

A: given(a)f(x)=ex(x2+2x-1)f(1)=e1(12+2(1)-1)=2ex0=1f'(x)=ddxex(x2+2x-1)f'(x)=exddx(x2+2x-1)+(x2+2x-1)d…

Q: Exercise 2. For each function, find a formula for the inverse of f. a) f(x) = 1+ 2e* b) f(x) = log;…

A: Given the function

Q: Use cofunctions of complementary angles to find θ where cos(17deg) = sin(θ). Use logarithm…

A:

Q: Find the inverse function of the given function. g(x)= 3- log, (16-x) h(t)= 3(42-)+ 5, where e is…

A:

Q: 2) If x=0 and y=5 Check if the following statement is true. Explain and show your work. log, (5x –…

A: log of negative number does not exist

Q: Find a formula for the inverse function of h(x)=2e3x . Verify that h-1(h(0))=0

A:

Q: Prove that the inverse hyperbolic function can be written in terms of logarithms: cosh¹x =…

A: We have to prove that cosh-1x=lnx+x2-1 for x≥1.

Q: Let f(x) = - x - 4x + 13 , x< - 2. Find a formula for the inverse function . %3D f"(x) = D -1

A: Given data

Q: 2. Use the product property of logarithms to write as the sum of logarithms. Simplify where…

A: Given,  a  log464xy  b log100z clog22m.4n  We have to write the logarithms as sum of  logarithms.

Q: Solve for x: log, x Vlog, * [A] –6, 1, 6 [B] 0, V6 [C] 0, 1, 6 [D] 1, 6 ||

A:

Q: Use composition to verity that f (2) = logi(z-5) and g (z) 3 +5 are inverses of each other. Show all…

A: f(x) and g(x) are inverse of each other if (fog)(x) = xand (gof)(x) = x

Q: Are functioNS fax) - inverse of e ach other and ga) %3D %3D

A: f(x)=x2+xg(x)=2x1-x

Q: O19 find the Value of X that Satisfies the following equation: a). log 10 Cx+2) + logio (x-1)-1 b).…

A:

Q: Drag the tiles to the correct boxes to complete the pairs. Match each equation with its solution.…

A: We know log a + log b = log(ab) log a = log b ⇒ a=b ea=eb ⇒ a=b log a = b ⇒ a=10b

Q: Let z = 2iand a = 1 –.For the first four subquestions (A to D), you need to have za. Remember that…

A: The given value is, z=2i,  α=1-i A. We have to find the zα, zα=(2i)(1-i)     ≈5.9054+9.7505 i   B.…

Q: 2x 1. Given the functions: f(x) = log, x, g(x)= 5-x x²-9 k(x) = and j(x) =9- 3x, %3D %3D g(x+h)–…

A: