2. The domain of the function y = 2159 / (k+1 - x^2)^(0.5) where k e R and k > -1, is:

Q: the estimate of solution to x=2^-x to 4 decimal places is what?

A:

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: 'the line tangent to the graph of y= In(3x) + 2x e at x=1 6 Jx-1 by using quotient rule. Vx +1 for…

A:

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

A:

Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2). If ƒ (2) = 7, what is…

A: answer is in next step. please give a like!!

Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

A:

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

A:

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

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Q: 2- Find the positive root of f(x) = xe"- cos(x) with an error tolerance =0.005% by using the secant…

A: Using a graph, it can be found out whether a function has solutions if the graph cuts the x-axis at…

Q: 10. f(x) = cos (2x)e*²-1

A:

Q: 2. Find the first derivative given that f(x)=x√√x + 1 x²√x

A:

Q: y = (Arccos 3x³)³

A:

Q: 5) Find the second derivative of f (x) = %3D ex plify your answer as much as possible

A: fx=1-2xexTo find the second derivative

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: The maximum value of y = cos x for - < x< is 1

A:

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Compute the second derivative with respect to x of 3x3 + 8 y = at x = 1.

A:

Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: 4. Find the length of the arc of f(x) = ÷ (1+ x²)ē between x = 0 and x = 3. %3!

A:

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 70x + 0.7x² –…

A:

Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: 12, for f(x) n(x) Estimate the slope of the tangent line at the point x (Use decimal notation. Give…

A: Given,

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: 4. Compute the second derivative with respect to x of 3x³ + 8 y : at x = 1.

A:

Q: By using the definition of the derivative find to f "(x) 3x3 +1 1 Ve +1 x +1

A: 1. We solve first order derivative of f(x)

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: Approximate the derivative of f(x) = x² + 4x + 5 at x = 3 using the forward, backward, and central…

A: f(x) = x2 + 4x + 5 h = Δx = 2 xi = 3         f(xi) = 26 xi+1 = 5          f(xi+1) = 50 xi-1 = 1…

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

A:

Q: Find the derivativeof the following function:

A: To determine derivative of the function.

Q: 2. Prove from the definition of derivative that for n EZ, d ng"-1 dr

A:

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

A:

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

A:

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

A:

Q: f (x) %3D х3 -Зх2- 2 3x2

A:

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: The derivative of the function f is defined by f'(x) = (x² + 2) sin (2x − 2) . If ƒ (2) = 7, what is…

A: Given f'x=x2+2 sin2x-2. Also given f(2) = 7.   To Find: The absolute minimum value of the function f…

Q: 9. Consider the interval [0, 2n] for the function y sec x. State an x- value at which the…

A: Given query is to find value of x for different conditions for instantaneous rate of change.

Q: The value of the second derivative of at its point of inflection is A less than zero B equal to zero…

A:

Q: So far, you've examined the function y = In x and its derivative, y' = , for large values of x. Now,…

A:

Q: 1. Show a numerical method of approximating the instantaneous rate of change at x = 3 for the…

A:

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4. ii, Find…

A: The objective of the question is evaluate area and find derivatives of given functions.

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

A:

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: Find the exact value of the function: 0 6 arccos (-/-)

A: See this solution in below

Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

A:

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…