5. The natural logarithmic function f(x) = In x has the .asymptote x

Q: (x cos x (а) у — etan(x³) + log;(e7 – x)

A:

Q: What is the (VA) Vertical Asymptote(s) of the function f(x) = log2 ^(x-2) If possible, please…

A: Given:

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: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

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

A:

Q: The effect on the graph of y = log,z if it is transformed to y = log,(z+3)? may be described as Oa…

A:

Q: 22. Express the signed area between the graph of y = - and the x-axis from x = 0.25 to x = 1 in…

A: Consider the given information. y=1x And, the given interval is 0.25,1. The area is defined as,…

Q: The derivative of the function y = log2(In(x)) is: 1 1 y': x In 2 In x y' = x In 3 ln x the above…

A:

Q: 1-In (-) + In(2x) = In3 2- 4 log 2 - log3 + log16 = x 3-Expand In [x? sin x /Vx2 +1]

A: To find the value of x

Q: 4 Evaluate (logyx)'., having given, 1 1 y = log1,x + ; log,0x + log10x + . 00 1+3+5+ ..+ (2y - 1) 20…

A: We have to solve given problem:

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: dx aluate: :S₁ (x+1) log(x+1) A In10 In[log(x+1)] + C 1 B -In[log(x+1)]+C In 10 O In 10 log² (x + 1)…

A: Topic:- application of integration

Q: Assuming that f(x) is defined for all x+0 such that x is a real number, what is the anti-derivative…

A:

Q: Let f be the exponential function defined by (2+2) f(2) = () and determine the folloving information…

A:

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

A:

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

A:

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: 5. Find the derivative of the following Natural Logarithm functions f(x) = In(3x – 4) a. b. 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: 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>0

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

A:

Q: 4. Show that id 5D accuracy is required to calculate the value of log(1+x) at x=0.1,0.5 by using the…

A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

Q: 5. Which of the following functions grow faster than In x as x →o? Which grow at the same rate as In…

A: Hey, since there are multiple subparts posted, we will answer the first 3 subparts. If you want any…

Q: Suppose y m In(x) + b is a logarithmic function that has the points (12.5,2.4) and (62.3,8) on its…

A: We have curve y = m ln(x) + b And it has the points (12.5,2.4) and (62.3,8)

Q: Suppose h(x) = log (2 -;) What is the correct result of the derivative of h with respect to x? A…

A: use logarithm to find the derivative.

Q: 7 log.y- log, w+4log.z 5

A: on applying log algorithm we will get

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: Show that (1+:)'→e. as x → o, → e. HINT: Since the logarithm function has derivative 1 at x = 1, %3D…

A:

Q: 17. The product rule does apply when multiplying exponential functions with sinusoidal functions.

A: Yes the product rule applies when multiplying exponential functions with sinusoidal functions

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: Suppose a Lorenz curve for a particular country is f(x)=x7/3 for 0≤x≤1. What is the Gini index of…

A: To calculate the Gini index using the Lorenz curve equation

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

A:

Q: Find the derivative y = 2* log3 x xln3 2* log3 x + xln3 (In x) · In 2 In 3 + n 32 x-In 3 None of…

A: At firts apply base change formula for log3x. Base change formula is logba= logea/logeb. Then find…

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: Evaluate y for the fx)= 4"-5 log,(x) 4*ln 4- Inx 4- x In 9 4- In 9 4'ln 4- x In 9

A: Answer

Q: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A: Consider the provided question, Suppose a certain population is initially absent from a certain area…

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

A:

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: rewrite each expression as a singlelogarithm.

A: 35). Given expression is 3log2x+log2y To rewrite the expression as a single logarithm. Solution:…

Q: Use l’Hôpital’s rule to find the limits

A: Given: The limit expression as limx→∞log2xlog3x+3, To find: The value of limit using L'Hopital's…

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

A:

Q: Find the equation of the vertical asymptote f(x)=log(x+4

A: We have to use properties of log function to solve the problem.

Q: Prove the following equation(with appropiate restrictions on the variables) logx–2=log(x/e²)

A: Here we will use the following formulas logab = log a -log blog(ax) = x log alog e = 1 Consider…

Q: 4. y = log v2x + 55. y = In(2x + 1)*6. f(x) = In(x +3)* %3D

A: topic - derivative of a function

Q: that the logar log x, and f(x) = In x have in common and the attributes that make them different.…

A: The difference between log and ln is that log is defined for base 10 and ln is denoted for base e.