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

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

A: Solution

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: (ii).Given that log, (y-1)+log, = z and log, (y+1)+log, x= z – 1, Show that y = 1+8° and find the…

A: Given: log4y-1+log4x2=zlog2y+1-log2x=z-1 . . . . . (equation 2) Concept: Here we shall use the…

Q: 8. In V5x 3 y z2 9. log. V xt 10. loga Va b5

A:

Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

A:

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A:

Q: 11-e18 x x+log3¤ Find y' where y =

A:

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: What is the value of ln[f'(2)] if f(x) = e^x?

A:

Q: dz dz +y дх = 50 +x4°y+y5° ), Prove that x ду If z= log (x50

A:

Q: Suppose h(x) = log 2-. . What is the correct result of the derivative of h with respect to x? In (5)…

A: Solve for the derivative

Q: 2. Differentiate: a) y = log2(3x) %3D 2 b) f(x) = –7 log(x²) %3D

A:

Q: Q2) find the derivative of the functions : 10 logą t (3x²-1 1) y 2) f(x) = 2x+5

A:

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

A:

Q: Differentiate the function

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

Q: 5. Find y' and y". f(x)= log,0 x Find y' if y=In(x²+y?) 6.

A: f(x) = log10x ∴ f'(x) = 1/x and f"(x) = -(1/x2)

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: Disprove the statement log(x + y) = log x + log y by, a) Letting y equal a positive constant of your…

A: Given  The statement log(x + y) = log x + log y

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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: Consider the function f (x) = log10 x.  Find the ratio of x1 to x2 given that f (x1 ) = 3n and f (x2…

A: Given, f(x)=log10x To find the ratio of x1 to x2 given that f (x1 ) = 3n and f (x2 ) = n.

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: Q2 Let X,X, f(r;8) = e/",I > 0. (i) Show that f(x:0) is a member of the exponential class. (ii) Find…

A: X1, X2, ...., Xn is a random sample from f(x,θ). We first calculate the likelihood function. If it…

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

A:

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: O f (x) = – log(x – 2) - -

A: Given: The functions, f(x) =12x - 2f(x) = log2 ( x +2)f(x) = - log ( x -2)f(x) = ln x + 2 f(x) =…

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: At what value(s) of x does e^(-x2) =x2 - x + 1?

A: To determine the values of x at which,

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: If fx) = r t 1 and g(x) = 8+x logx 1 what is the domain of (fx g)(x)?

A: To find  The domain of (f*g) (x)

Q: How large does x have to be, so that e^(-x/10)<0.1?

A: We need to find the values of x for which the following inequality holds good.

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: - y =log x² dy_ 8log, x A. dx dy 4log, x В. dx dy _ 4xlog, x xIn 2 dy 8x log, x D. dx xln2 xIn2 dx…

A:

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

A:

Q: 6. Which of the following functions grow faster than In x as x→∞? Which grow at the same rate as In…

A:

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

A:

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 h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to…

A:

Q: What is the derivative of the given logaithmic function y = log3 (2x“)? 2 In (3z) 2 A. æ In (3) 2 В.…

A: Let's find.

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: 2. Find the derivatives of the following functions. a) y = (log2 x)3¬*

A: Given information: The function is y=log2x3-x. Calculation: Find the derivative of the function. Use…

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A:

Q: Find the derivative of the following: 8 f(x) = 3 (log5 ( – 2/x7 + x))* - e(v3³n²)

A:

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: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

A:

Q: Eхample 33. x" log x dx .

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.