Find the equation of the vertical asymptote f(x) = log(x – 1)

Q: (h) lim - 7 log: (z) -0- ||

A: Given query is to find the value of indicated limit.

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

A: Given:

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 logarithmic function f1x2  ln1x  12 has theasymptote x

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

Q: The asymptote(s) for the function y = log(-x + 2) is a) and the asymptote(s) for the function y =…

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: At what value(s) of x does ln (1 - x2) = x - 1?

A: We need to find the solution of the equation given by

Q: solve: loga (4x+4)= log₂ (-7x+19) = X= AS lenter DNE if no rolution)

A: topic - logarithmic equations

Q: Calculate the limit of log3 x as n – ∞ O 3 8

A: There should be correction in the question that x tending infinity.    As there is nowhere 'n'…

Q: log(1+e¯*) is The indeterminate form of lim,→∞

A: The form is:-

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

A:

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

A: Given

Q: The equation y = log(x – 3) has a vertical asymptote at: X =

A: The graph of log(f(x)) has a vertical asymptote at the value of x such that f(x)=0.Example: for…

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: sketch the graph of f(x) =1 log2 (x+3)  state vertical shift, horizontal shift, ordered pair where…

A: The given function is f(x) =log2 (x+3)To sketch, state vertical shift, horizontal shift, ordered…

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

Q: The natural logarithmic function f(x) = In x has the asymptote x =

A: Given: f(x)=lnx To Find: Asymptote of f(x). Concept: Vertical Asymptote: x=c is called vertical…

Q: Prove: logaxr = r loga x.

A: Given equation: loga xr=r loga x

Q: Find the exact x-coordinate where there is a horizontal tangent line to the graph of f(x) = x10°.…

A: Given,          The function is fx=x10x.

Q: Q 3/ A- Find lim,3 B- log10 (3x – 7) + log10(3x + 1) = 1+ log10 2

A:

Q: The exponential function f(x) = ()* has the asymptote y = This means %3D that as x 0, we have ( -

A: f(x)=12x

Q: write the logarithmic equations in exponential form.

A: Since, you have asked multiple questions, we will solve the first question for you. If you want any…

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: 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: 2 lim log 10* X-1 8. -3 lim log,(x-2) x-9 А. 3/2 В. 2/3 C. 1/3 D. DNE

A:

Q: 5. Sketch a graph of the function f(x) = 3 log(2x – 2) +4. Identify the key features. a) domain and…

A: The given function is: fx=3log2x-2+4 The logarithm is defined only for positive real number.…

Q: Sketch the graph of the function f (x) = log.(x + 2) + 3, where c > 1. State the Domain and Range…

A:

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: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=lnx,  gx=ln2x

Q: 5x + 2 lim log + 6 10x + 12 ° X-

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: Find the equation of the parabola osculating with the exponential function f(x)=ex at the point…

A:

Q: The equation y = log(x – 5) has a vertical asymptote at: - X =

A: Consider the equation  y=logx-5

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: What is the linear approximation of log base 5 x at x=5

A:

Q: The natural logarithmic function f1x2  ln x has theasymptote x 

A: Graph of f(x):

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: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: We know that from the limit method, a function fx grows faster than gx if and only if limx→∞fxgx=∞…

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

A: topic - derivative of a function