4. Draw the following graphs: a. y =1-cos(2x) b. f(x)=1 x2 if x<1 3-x if x 21 d. f(x)=logx c. y=2e*

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

A: Solution

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

A:

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

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

Q: dy et y = (x³ – 18x)m(=). Find using the method of logarithmic dx - ifferentiation. Express your…

A: Topic:- derivatives

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

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

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: | 1-x² y = log10 2- 5x

A:

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

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: Find , given y = log(ev+x²). dy dx

A: Given y=logex+x2  We find dydx The differentiation formula of logarithm is ddxlnx=1x and the power…

Q: Find ay dx 3. 4. 5. y = 2e³x5tanhx y = xln(5x-2) y = sec ¹(log 7x)

A: Given :y=2e3x5tanhx4. y=xln(5x-2)5.  y=sec-1log7x

Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

A:

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: at any point h (1, 1) is logx – x

A:

Q: 1. Find the function of the form y = log,(x) whose graph is given. y = y 1.5 (5, 1) 1.0 0.5 5 6 -0,5…

A:

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: Sketch on graph a) y = 2x-3+ 3  b) y = log2 (x – 4)

A: a)

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

A:

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: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

Q: dx Evaluate log - 1+ax 1-ах

A:

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: Differentiate the following and simplify: y= log, (sinhe") h(x)=3sinh(1–3x² )cosh(1– 3x² ) 1. 2.…

A: As per bartleby guidelines we only give first question answers.

Q: Find h" (x) if h(x) = log,(cos(x)) – e®z. -

A:

Q: 26. Describe the behavior of each of the following: (a) 5 (b) log x as x>0 as x (c) ln x as x ->co…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: Find the integral: log2 X dx In(2)/ 082(x) + C 2

A: Put logx = u then solve it.

Q: 1. Which of the following functions grow faster than e* as x→∞? Which grow at the same rate as e"?…

A: Dear students,  Please find the solutions of 3 parts. In case you need help with the other questions…

Q: 2. Compute for the value of x in a given logarithmic inequalities loga(x+1) > log:(x2). a. x > ½ b.…

A:

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

A:

Q: If y = loge(sin x)? dx will be equal to dy

A: Given: y=logesinx. To find: dxdy Solution: Chain rule of differentiation states that:…

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: 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: 4.) Find y': Given:y = x²(3 cosh x - 1) 5.) Find y': Given: y = log, csc h (6x³)

A:

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

A: Consider the equation  y=logx-5

Q: Find d (7ª). Type In(x) for the natural logartihtm function. dx

A: Given query is to find derivative if the expression.

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: 3. (a) Calculate sinh (log(5) – log(4)) exactly, i.e. without using a calculator. Answer:

A: Solution is given below:

Q: 1. Express the following as a single log 3log xy-log x +log y a) 6log x b) 3log x c) 6log y d) 3log…

A:

Q: 2) Find y for each problem dy a.) y= lo9, (3+ arc COs x) DASC OF iyarithm Y= log, (3+ arc cos x *5is…

A:

Q: dx Evaluate: s (x+1) log(x+1) A --In 10 log² (x+1)+C 2 B In10 In[log(x+1)] + C с = -log² (x + 1) + C…

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: Find d/dx(4^x). Type ln(x) for the natural logarithm function.

A:

Q: 8. Without a calculator, match the functions y = 2, y = e, y = 3, y = In x, y = log x with the…

A: Without using a calculator, to match the functions, y=2x, y=e-x, y=3x, y=ln x, y=log x with the…

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

A: topic - derivative of a function