3) Differentiate: (Do not simplify or plug in any numbers); You must use the chain rule where required. If necessary rewrite the function before you use the rules. 1 a) (6x² -10x+3)!! b) (2x² – 7)* 1 đ) V(4x² +1)" (4x² +1) e) In(x*+1) f) 50eB*) g) 3000(76×) h) log4(3x³)

Q: g(x, y) = In(2-x) 1-x2-y²

A: To find the domain of the function, g(x,y)=ln(2-x)1-x2-y2

Q: Use the graph of f(x) = x3 + 3x2 - 4 in the figure given to factor x3 + 3x2 - 4.

A: Given function: And the graph:

Q: 31. f(x) = 2x3 -3x2-36x %3D

A: Given the function f(x)=2x3−3x2−36x

Q: 8х + 7 State the domain of the function f(x) = in interval notation. 9х + 2

A: A detailed solution is given below

Q: How can you sometimes handle limits that lead to indeterminate forms 1∞, 00, and ∞∞? Give examples.

A:

Q: Discuss the continuity of the function on the closed interval.                              g(x) =…

A: We can not have a negative value under the square root.  So,

Q: What is the local maximum value of the f(x) = x3 - 3x +2 on [0.5, 4]

A: We are given the function  f(x) = x3 - 3x +2 on [0.5, 4]. Here, we need to find the local maximum…

Q: 4х+7 (ii) If f(x)={ 1<x<2 determine whether the function f(x) is continuous 14x² -1 2<x<4 throughout…

A: Continuity of the function

Q: Exercises 73–75 will help you prepare for the material covered in the next section. 4 73. If f(x)…

A: (73).              f(x) = 4x-3                     substitute x =3,                     f(x) =…

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

Q: 7. Differentiate f(x) = (3x + x)² in three ways. When you have completed all three parts, show that…

A: Given that, fx=3x+x2

Q: Find the absolute maximum value of y=sqrt(16-x2) on the interval [-6,6]

A: y=16-x2         -6,6y=16-x212ddxy=1216-x212-1.0-2xdydx=12-2x16-x212dydx=-xx116-x2Now , dydx=0…

Q: Example 2: Using the False Position method, find an approximated root of the function: f(x) = x² –…

A: The equation in form f(x)=0 is called a transcendental equation. If the function is continuous on…

Q: How do you solve question 4?

A: We are given the function, f(x) = x4 – 2x2 + 3x. Here, we need to show that the function f(x) has a…

Q: Find critical number of f(x) = x^2 - 6x + 8

A: To find critical number of f(x) = x^2 - 6x + 8

Q: What is the average rate of change of the functin g(x) = 2x^2 -9 on the interval [4,7]

A: g(x)=2x2-9 on the interval [4,7]

Q: Prove that a function of the form:is an even function.

A: The given function is  y=a2nx2n+a2n-2x2n-2+...+a2x2+a0

Q: Find the limits in Exercise

A: Find the limits x→-∞lim(2x+(4x2+3x-2))

Q: Prove that lim(4x² – 25) = -9 X-2

A:

Q: 4. Determine the number of zeros of the function f(2) = 224 – 2iz³ + 2² + 2iz – 1 in the upper…

A: The complete solution is in given below

Q: Present a combinatorial argument to justify your answer. How many functions are there from {1, · · ·…

A: Consider the given information as, 1,⋯,n to 0,1

Q: Find the limits in Exercise

A: Given,          limx→-1416x13x+162

Q: 5. Use limits to derive f (x) = 4x² +

A: We will solve the problem

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: You are not allowed to use L'Hospital's Rule 2x2 – 32 - lim V3x + 4

A:

Q: 8. Determine the limits as x approaches infinity. 2х3+1 3 а. -3x3-3x2+7 x°+3 С. х2-2 3x b. 2x2-1

A:

Q: check uniquness and existance for fixed point while f(x)=(2x+1)^-3 in [1,2]

A:

Q: a- Find the limits of the functions below: 7x3 - limx→0 3-3x²-6x x+2 limx--2 Vx²+5-3

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

Q: Help Solve in Product Rule find f’(x) and f’(c) ; g(x)= x^2 - 4 / x + 3 , c=0

A:

Q: Prove that lim(4x2 – 25) = -9 x-2

A: First we use the formula a2-b2=(a-b)(a+b) then put the limit.

Q: Help with this problem?

A: The given function is f(x) = 5 + 7xTo find the value of x for which |f(x)| = 5.

Q: what should n be if f(x) = Xn defineof a polynomial function?

A:

Q: 3. In your own words, explain the Squeeze Theorem.

A: Squeeze theorem is a calculus theorem related to limit of a function

Q: By using intermediate value theorem locate a root for the f(x) = 2x3 - 3x2 - 6.

A:

Q: Evaluate the limit 7x2 2.0 2x +3 lim 3x +4

A:

Q: In the Algebric terms what is meant by nvertible function?

A: Invertible function:

Q: Let f(æ) = Vr² – 5, g(x) = , h(x) = go((gof)+h(x)) at x=-1? Find - %3D 22-9

A:

Q: Find the function g such that fog = In (2x° +7) if f(x) = In x g(x) = %3D

A: Find the function g such that  f(g(x))= ln(2x3+7) and f(x) = ln(x) .

Q: Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the closed…

A:

Q: The function fin) = 8n-2 is big-O(n). True False

A: Consider the given function.

Q: By using intermediate value theorem locate a root for the f(x) = 2x3 – 3x2 – 6. %3D

A:

Q: 13. Use the Intermediate Value Theorem to show that f(x) = 2x° – 3 has a zero in the interval [1,2].…

A: Given:-f(x)=2x3-3 using the intermediate value theoremf(x) is continuous in the interval 1,…

Q: Find critical number of f(x) = 4x^2 + 8x -1

A: We have to find critical number of  f(x) = 4x2 + 8x - 1 To find critical number, differentiate f(x)…

Q: Show that the equation x - 17x +c = 0 has at most one solution in the interval [-2, 2]. Let f(x) = x…

A: The given equation is : fx=x3-17x+c The given equation has at most one solution in the interval…

Q: 8х + 7 State the domain of the function f(x) in interval notation. 9ж + 2

A: Given,f(x)=8x+79x+2

Q: 4. Determine the number of zeros of the function f(2) = 2zª – 2iz³ + z² + 2iz – 1 - in the upper…

A:

Q: ,3]---->R F(X)=2X-3 من المعلومات .A (7,5-, 3-, 1-, 1,3) .B (-7, -5,3-, 1-,1,3-) .c (-7,-5,-3,-1, 1,…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.