6. Find the domain of f(x) = log, [log, [log3(18r – x² – 77)]]

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

A: Solution

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: 6. The logarithmic function f(x) = In(x – 1) has the asymptote x %3D

A: Given, Logarithmic function, f(x)=ln(x-1)

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: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: a- Simply the following 1 1. Inx – In(x2 – 1) + 2ln(x + 3) - 2. 5log2 + log3 – log8 b- find x for…

A:

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: f (t) is of exponential order at infinity.

A: By fundamental theorem of calculus, we have f(t)=f(0)-∫0tf'(u) duAlso, since f' is piecewise…

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: log(2² – 2y² – 4x²) In(2 – |2|) - g(x, y, z) = -

A:

Q: 2. The function f(x) = log, x is the logarithm function %3D So f(9) = -- f()- with base %3D f(1) =…

A:

Q: 6. h(t)=- 2-1 7. g(x)%= 1-Vx-2 8. f(x) tanx 9. (x) = log(1-2x) 10. y (1-x

A: Please check step 2 for the solution.!

Q: If k is a positive constant, show that x^2 e^-kx approaches 0 as x --> ∞.

A: Given  The x2e-kx approaches 0 as x→∞.Where k is a positive constant .

Q: Differentiate the function

A: Before we get into solving the question, let's look at the two derivtives shown on the white…

Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

A:

Q: 4. Differentiate the function. f(x) = log3 (x In x)

A:

Q: Q7. Differentiate with respect to x: (a) log (x), *). cOS X

A: 7(a) Given- logcosxsinx To find- The derivative of the above expression with respect to x. Identity…

Q: dy : Prove that dx or ỹ for expression y log2(x²) is equal to ỹ = 2[1-log2 x² In 2] %3| x2 x³ In 2

A: Given, y = log2x2x2    We have to prove dydx or y¯ = 21-log2x2.ln2x3ln2

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: 4. f (x) = log2 x and g(x) = vx – 4. What is the domain of f( g(x))and g(f(x))?

A:

Q: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 2

A:

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: 22. Suppose f(x) = log x + log(x – 3). Find the x-value for which f(x) = 1.

A:

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

A:

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

A: Let's find interval when both functions are negative.

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

A: Derivative of function f(z)=Log(g(z)) where g(z) is some complex function. f'(z)=g'(z)g(z)…

Q: Find the derivative f'(x) if f(x) = log 3x² A. (2/x) log 3x B. (2/x) log e C. (3/x) log 3x D. (3/x)…

A: Solution

Q: =) Express the new function h(x) log2 in terms of the original function f (x) log, (x).

A:

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

A:

Q: 5. Find the domain of f(x) = log(x-4)

A: The given function,   f(x)=logx-4

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: Find the range of the function x* +e x+e f(x)%3sin{log, +cos {log. x' +1 2 x*+1

A:

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. O True…

A:

Q: 3. Find syz for ys = In(x + yz) – xcoth- log ()-

A:

Q: Differentiate the following functions f(t) = ln | cos(ln t)| f(x) = log2 (x10ex) y = ln(( etan…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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: . Consider the function g defined by 1 g(x, y) = cos (Tx y) + log3 (x - y) Do as indicated. 1.…

A: As per policy, we are allowed to answer only 1 questions at a time. So, I am answering the first…

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

A: