f(x + h) – f(x) h\1/h log 1 + If f(x) log, x, show that = h + 0. h

Q: If w=log(ysinx+xsiny) then prove that wxy=wyx

A: If w=log(ysinx+xsiny) then prove that wxy=wyx

Q: 9. What is the maximum value of |Log z| |2| 1? on

A:

Q: Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o…

A: Given

Q: let f(x)= x^5x where x>0. use logarithmic differentiaiton to find f'(x)

A:

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: A function g has rule g(x) = log, (x-3) + 2. %3D а.

A:

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f)= log(x²+1)-log(2) on [-1,1]is:…

A:

Q: 2. The function f(x)= log₁0x has the point (10, 1) on its graph. Find the coordinates of the image…

A:

Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: 3. Use Log Rule to integrate. a. Sor5 Sdx а. бх-5 b. S; -dx x(lnx)²

A:

Q: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: Find the domain of the function of 5 log₂ (4-x²)+11 f(x) = 12x-31-2 + sin¯¹(1 − 2x) Express your…

A:

Q: Differentiate the following functions: 1. y = tan(log25x) + x. log3(sec x) 2. logyx = logxy %3D

A: We havey=tanlog2 5x +x.log3 (sec x)Let  u=tanlog2 5x     and    v=x.log3 (sec x)Now y=u+vdiff.…

Q: () N f(x) = , show that f(0) and its leading differences form a geometr 5. (i) Prove that A log x…

A:

Q: (3) Find the domain of f(x) = log(6 + x – x²) (A) (-∞, 3) (B) (-2, 3) (C) (3, ∞) (D) (-∞, -2) U (3,…

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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: If H(x) = logb 1/x, show that H(b-1/z)= 1/z

A: H(x)=logb1x, we have to show that Hb-1z=1z

Q: Solve for z.  Log(z)=1-i   (Also, is there a case where there are four distinct solutions?  Or…

A: Given logz=1−i We have to solve the equation logz=1−i for z Use logarithm property  logm=n⇒m=en

Q: f (x) = In(x + 4) + 3 %3D f(2) 3 e2-6- 4 %3D f (x) = log(a- 2) - 8 %3D f (x) = 108+2 ----- f (x) =…

A: Some functions are given and the inverse of the functions are also given. We have to check that…

Q: 1. Let f(x) = log2(x). II

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Q: Prove that | log,x| E O(log2 x )

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: To Discuss: a. Does fx=logarithm x, with base 12 approaches a certain real as xincrease positively?…

Q: 10. Prove that (log2 3)-1+ (log4 3)-1 < 2.

A: Simplify the powers of the term (log23)-1+(log43)-1 by writing the terms as fractions.…

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: Show that J log(1 + tan0)d= log2

A: Given that: To prove:        ∫0π4log(1+tanθ)dθ=π4.log2

Q: Prove that In x lim xP for any number p > 0. This shows that the logarithmic function approaches…

A: Prove that limn→∞ ln xxP=0for any numbers P&gt;0

Q: The value of c which satisfy the conclusion of Rolle's Theorem for f(x)=log(x²+1)-log(2) on [-1,1]…

A:

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

A:

Q: 14. Find the domain of definition of the function 31 Vx + 5 X-5 y = log10 (,2 x² – 10x +24

A: The domain of a function is the set of input or argument values for which the function is real and…

Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

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: Find all x- and y-intercepts of graph of y = -3 +log2(x2 - x +2).

A: Given function is y=-3+log2x2-x+2

Q: 13. Determine whether or not each statement is true or false for all x>0 & y> 0; If a statement is…

A:

Q: 6) Given that x = log, b. write down an %3D expression for b in terms of a and x. log, t that log, t…

A:

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: п/4 Show that log(1+ tan8)d = log2. 8

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Q: solve for x, log(x+5)-log(x+2)=2 please show work.

A:

Q: Consider the function g defined by 1 g(x, y) = cos (Tx VT) + log3 (x – y)" Determine

A: We can solve this as follows:

Q: 2 log(x+y) = 3log3 +logx + logy

A:

Q: 6) If u = log (x² + y²), then prove that log (x² CSScanned with CamScanner dydx ôxôy

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Q: log x" -[x] [x] Evaluate : lim where, n e N and [] denotes the greatest integer function.

A:

Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

Q: Prove that A log ƒ (x).= log|1+A7®) f(x)

A:

Q: 12) eiven AMUEÍVRTAMA, S C«) X22x<0 2x+1, 0<xL2 a) Evaluate f at x = -1,0, and 5. If not defined,…

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Q: d log, x = 1 dx [(In a)(x)]

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Q: Find of, af , for f(x, y) = log₂ (3г² - +y)

A: Solution of given question is written in below steps.

Q: Determine if the function f(x) = {(x2 − x)4/3 , if x < 1…

A: The objective is to check the differenriabiliry at x=1.

Q: (a) Prove that log₁ x= -log₁ x where a > 1. a

A: