find and sketch the range of the function g(x, y) = ln(x ^2+y^2-9)

Q: Differentiate the function. f(x) = 5x ln(3x) − 5x

A:

Q: Find the average rate of change of the function from X1 to X2. f(x)= -3x2-x from X1= 5 to X2= 6

A:

Q: Verify f(x). direction delta function 8(x - a)

A:

Q: Implicit differentiation of x^2y^2=4

A: we have to find the implicit differentiation

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We have to find average rate of change of the function f(x)=6xr+y on [x, x+h]

Q: Locate any relative extrema and points of inflection. Use a graphing utility to confirm your results…

A: Here, By taking derivative Now, find a critical point by considering y’=0

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)

A: To find the antiderivative we integrate the given function c=integration constant

Q: Analyze the graph of f'(x) (first derivative) Find all extrema. Determine which are maximums and…

A:

Q: Differentiate the function. f(x) = ln  7   x f '(x) =

A:

Q: valuate the second derivative of the function at the given point. Use a computer algebra system to…

A: The derivative of the square root function is calculated using the formula ddxxn=n·xn-1. The value…

Q: Calculate root and error %. Find the root of the equation fx=ln(x)-5+x in the interval [2.5, 3.0]…

A: Consider the given information.

Q: Consider the function f(x,y)= 2-x* +2x² – y² Find the critical points of f. Use the second…

A: At first we calculate D=fxxfyy-fxy2 at each critical points. If D<0 the critical point is a…

Q: State the limit of the derivative f’(x) = square root of x+3, f’(2)

A:

Q: Integration is the reverse process of differentiation.

A: Given,            Integration is the reverse process of differentiation.To find : State true or…

Q: Find the derivative of the function. State the domain of the derivative. f(x) = [In(x)]6 f '(x) =…

A:

Q: 75. F(x) has a negative derivative over (-, 2) and (5,9) and a positive derivative over (2, 5) and…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: How do I differentiate this function using the chain rule: f(x)=[x^2/sin(x)]^6

A: Given,           The function is fx=x2sinx6.

Q: In 2x -dp-

A: To evaluate the integral: ∫2ln2xxdx Solution: Let substitute t=ln2x. Differentiating both sides, we…

Q: derivative of √x²-4 - 2arcsex x/2, 2<x<4

A:

Q: ) Calculate the derivative of f1 (x) = 2x4 - 3x3 + 1/2x2 + 3. b) Study the sign of the derivative…

A:

Q: Find the average rate of change for the function over the given interval. y = x3 - 3x2 + 5 between x…

A: The average rate of change of a function f(x) from x = a to x = b is

Q: Qa/ Explain the rule of maximum and minimum using Derivatives with an example?

A:

Q: (3) A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x. Each…

A: Length of wire = 10 cm

Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…

A:

Q: Find an absolute minimum and absolute maximum,find a local minimum and local maximum, find the…

A:

Q: derivative of f(x)= arcsin(3x^2)arccsc(2x^3)

A:

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A: The given function is, fx=54x4+203x3-452x2-180x The 1st order derivative of fx is,…

Q: equation of tangent line of f(x)=5x^3+1 at x=1 is * O y=15(x-1) O y=15 x-9

A: Given: The function f(x)=5x3+1 and a point x=1

Q: Find the relative extrema of the function h(x) = 2 tanh x − x. Use a graphing utility to confirm…

A:

Q: Which derivative rule is used to derive the Integration by Parts formula? A. The Integration by…

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Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A:

Q: For the drug metabolism function f(x) = -x(x+2)(x-3) , find the average rate of change of f(x) on…

A:

Q: Differentiate the function. f(x) = sin(3 ln(x)) f ' (x) =

A: To find the derivative of the function

Q: しx)f erentiate f メて ×ケ-X arcsin (3x -1)+ In (5x*+3) 6arctan (1-x) . メ9 fon

A: f(x) = sin-1(3x-1) + ln(5x4+3)

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The average rate of function f(x) on the interval a,b is given by  average rate of change = fb-fab-a…

Q: What is the anti-differentiation rule to be used in order to integrate the function f Vx5 dx. a.…

A:

Q: Find the critical point(s) of the function f (x, y) = xy + ln x + 2y . Then use the second…

A: Find critical points, nature of critical points  and relative extrema of the given function.

Q: Evaluate the derivative of the function for the given value of x. y = square root of x  / over…

A:

Q: Find the average rate of change of the function from x1 to x2. Function x-Values f(x) = −3x +…

A: Function      x-Values f(x) = −3x + 19      x1 = 0, x2 = 3

Q: e average rate of change of the function from Function X-Values f(x) = -2x3 + 8x2 + x X1 = 1, x2 = 8

A: Given : fx = -2x3+8x2+x

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: The given function is fx=2x2+5. The average rate of change of a function f over the interval x,x+h…

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A:

Q: Differentiate the function. h(x) = ex9 + ln(x)

A:

Q: Show that a constant function f(x) = b has an average rate of change of 0. Compute the average rate…

A: Average rate of change of constant function fx=b Rewrite;              y=b…

Q: Find the first derivative by increment method. Show your complete solution V7x – 12 Upload your…

A: The given function is 7x-12

Q: A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At…

A:

Q: Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).

A: The given function is: f(x)=(x)(1-2x)3 And, at point (1,-1), we have to find the equation of the…

Q: Differentiate the function. f(x) =  5   ln x f '(x) =

A: Given that: f(x)=5.lnx

Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…

A: We will use the average rate of change formula. f(x+h)-f(x)h

Q: Appy the second derivative test to find the absolute maximum value on (0, 0) for f(x) = 15-4x

A: Given function is, f(x)=15-4x-250x2

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.