Implicit Differentiation, Related Rates Problem 1. In this problem, we consider the Lemniscate curve (1) (a2+y2)2 =3(z2 - ) 2 -2 Figure 1: Bernoulli's Lemniscate The goal of this problem is to find the four points of the Lemniscate curve with horizontal tangent lines. 2 -2 a. Use implicit differentiation to find the expression for dx b. To look for those points, set up the equation 0 (you should find an equation of the type x2y2 with a horizontal tangent line belong also to a circle centered at the origin since they have the same distance to the origin); C, with C> 0,... Yes! because the four points + c. In order to find the y coordinates of the points with a horizontal tangent line, replace y in equation (1) by the value C found in part b. then solve the equation for y (Hint: to eliminate 2, use the equation x2y C again) 1 d. Find the I and y coordinates of the four points of the Lemniscate curve with a horizontal tangent line. 1

Q: ∭Ef(x,y,z)dV as an iterated integral in six different ways, where E is the solid bounded by z=0,z=5y...

A: It is given that the solid bounded by

Q: Help with 14.

A: To determine the winner from the given data about the race

Q: Find the slope, the x-intercept, and the y-intercept for each linear equation  a.) y=3x-24 b.) x/2-6...

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

Q: Find f'(x) and find the value(s) of x where f'(x) 0 X f(x)= X 25 f'(x) Find the value(s) of x where ...

A: Use quotient rule to find f'(x).Quotient rule: (u/v)'=(u'v-uv')/v^2Answer: f'(x)= (25-x^2)/(x^2+25)^...

Q: using L'Hospitals Rule, what is limx->(pi/4)+ 4sec(2x) - 4Tan(2x)

A: The given expression is:

Q: Use Gaussian elimination to find the complete solution to the system of​ equations, or state that no...

A: It is given that the system is  

Q: Given the following information, use synthetic division to find all roots of f and describe the proc...

A: f ( x ) = 2 x 3 + 21 x 2 + 49 x − 30This is a degree three polynomial, hence there will be three roo...

Q: 2.7 Can you show me the steps to solve step e? 1) f(t) = t^3 - 9t^2 +24t e) Find the total distance ...

A:

Q: 7 Exercise 5: Calculate the following limits, using the 6-e definition of a limit (i.e., provide an ...

A: Hey, since there are multiple questions posted, we will answer first three sub parts question. If yo...

Q: Use the truth statements to show the statements are equivalent logic, tautology

A:

Q: Find the absolute maximum and absolute minimum values of f(x)=(x^2−25)/(x^2+25) on the interval [−5,...

A: Given function,

Q: How do I find the x-coordinate of the point of inflection of f(x)=x(x-8(x)^(1/2))?

A: According to the given information the given function whose x coordinates of the point of inflection...

Q: 14. Find (A) the domain, (B) the intercepts, and any vertical or horizontal asymptotes for the graph...

A:

Q: Find the average value of the function f(x)=−3x2 on the interval [-1, 1].

A: To calculate the average value of the given function over the interval [-1,1]

Q: Let f(x)= x2/3(3x-6)2 Find the x-coordinate of the critical point(s) of f(x). Find the interval(s) ...

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3. Pl...

Q: (1 point) Find the absolute maximum and absolute minimum of g() t4-i on the interval [0.7,3.7] Enter...

A: Consider the given function:

Q: 5. Using the Taylor series of e^x about x = 3, find the first three terms of Taylor series andthe er...

A: Given, function

Q: I need help with question 13 in Section 3.6, page 223, of the James Stewart Calculus Eighth Edition ...

A: Given:

Q: Can you help me step by step?

A: Given function is

Q: Water is leaking out of an inverted conical tank at a rate of 11,500 cm3/min at the same time that w...

A: Given:

Q: g(x)=2x^3+5x^2-28x-15 A)find power function B) homany turning points can this graph have

A:

Q: see attachment

A:

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: Hi I need some help with this continuity problem Please cite the continuity theorems thank you

A: Given:

Q: exercise 11 part B

A: To identify the points where f(x) has a limit.

Q: we are supposed to find all these and i do not know how to do this. for this problem.

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

Q: Can you help me step by step?

A: Assume p=x^2*sin^9 xThen find derivative of p w.r.t. xUse product rule and chain rule for this.

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of t...

A: The given paramedic equations are,

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley ...

A: Refer to the question, from the above information one can note that the point where the rope touches...

Q: y=x(tan^-1)(2x)-(1/4)ln(1+4x^2) find derivative of the function: full steps please

A: The given function is

Q: How do I find the x-coordinate of the point of inflection of f(x)=x(x-(8x)^(1/2))?

A: To determine the x coordinate of the inflection point of the function f(x).

Q: Use the graph of f' to identify the critical numbers of f, identify the open interval (s) on which f...

A: As given curve is a straight line so f’ is a straight lineLet given line is

Q: f(x) = xlog4(22x)

A: To simplify the given logarithmic function.

Q: find the derivative f(x) = xππx

A: The given function is

Q: f(x)=2x divided by x2 +8x+15 Identify domain, x intercepts, y intercepts, all asymptotes. Identify r...

A: Hi, as per our norms, we answer three sub parts to a question. Since your question has seven sub par...

Q: 4) Solve the integral: Show work 10x2-48x + 160 dx (x - 4)2 (x2 + 16)

A: Given,

Q: Use the arc length formula to find the length of the curve y = 5x - 4, -1 s x s 2. Check your answer...

A: Given:

Q: find the derivatice of y=sqrt[sin(x^4-1)]

A: Consider the given equation

Q: Can you help me step by step?

A: Let y = f(u) then solves the derivative by applying the chain rule:

Q: 5. use the four- step procedure to find f'(x) 1 b) f(x)24x 2 a) f(x)

A: Use four-step procedure to find derivative of f(x).

Q: 1+ Sn 2

A: To evaluate the integral of the given trigonometric function

Q: In the Taylor series for the function 3x^2 − 7 + cos x expanded in powers of x, what is the coeffici...

A: Given:

Q: 2.6 Can you show me the steps to solve the problem? Directions: Find dy/dx by implicit differentiati...

A: Given, 

Q: Graph the function y=-3tan3x To draw the graph, plot two consecutive asymptotes. Between those asymp...

A: Given, function

Q: Sketch the slope graph of a function f with input t that meets these criteria f(-1) 5 the slope is p...

A: Given information:

Q: Please help with all three with corresponding answers to the problems.

A: a) For given function f(x)=x^2-6x+4, we find f'(x) and f'(x)  

Q: Use power series methods to solve the DEs below about x0. You may leave your answer in terms of a re...

A:

Q: I need help with number 8 part A-D. Thanks

A: Hello. Since your question has multiple sub-parts, so as per guidelines we will solve first three su...

Q: I am confuse on this Question please help.   A local bicycle shop placed older model bikes on sale l...

A: (1)The sales price is $274 and the normal retail price $585.Obtain the number of times as large is t...

Q: A cube with 35-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter...

A:

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.