What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

Q: 1 -1 -2 -2 -1 0 1 2 3 2 3 4 4 -2 -1 4. FIGURE 6.1.12. Spiral point (-2, 1) and saddle point (2,-1). ...

A:   Given the systemdxdt=2x-2y-4 anddydt=x+4y+3 To find critical point we take dxdt=0 anddydt=0  

Q: 3x²–10xy+3y²–32= 0 Rotate the axes so that the new equation contains no xy term. Analyze and graph t...

A: Given .  Equation 3x²-10xy+3y²-32=0 Let's assume that axis is rotate an angle theta. So new coordina...

Q: u³ = a²t , find d’u %3D dt3 2a4 а. 9u5 10a6 27u8 -10a6 С. Zu® 40a6 d. U8 b.

A: A detailed solution is given below

Q: Given the function y=f(x), y' is found to be negative over the interval (4,8), then over this interv...

A:

Q: Using the power series method, find the first five non-zero terms of the solution for the following ...

A:  Consider the solution of the function to be yx=∑n=0∞an·xn. Now, differentiate it with respect to x,...

Q: of the function at x=c. The second derivative of the function y=f(x) at the point x=c is characteriz...

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Q: Find the derivative of the vector function below r(x) = sin (secx ²)i +csc°(Vx² +1)j +8tan(x' k

A:

Q: second-order Taylor series expansion of function f(x)=ex g(x) at x=0 and calculate f(0,8) using this...

A: f(x,a) = f(a) + (x-a)f'(a) + (x-a)22f''(a)Here  x= 0 , a = 8So, f(a) = e8×g(0,8) = e8Since f(x) = ex...

Q: 1. Find the general solution of (y? – 1) = 4xy? dx dy 2. Find the solution of dx e2x+y that has y = ...

A: Using variable separable. Then integrate it .  According to guidelines we solve only first three par...

Q: dx -1 2x+3

A: To solve the following integral

Q: Write a chain rule formula for the following derivative. dw for w = f(x, y, z); x = g(r, s, t), y = ...

A: w=fx,y,z ; x=gr,s,t, y=hr,s,t, z=kr,s,t

Q: 1. A movie theater seats 240 people. For any particular show, the amount of money the theater makes ...

A: The given that the number of people in attendance is given by: n=240-12p...(1)  where the price of a...

Q: Prove: 1. tan (A/2) = - cos A 1 + cos A sin A 1+ cos A 2. tan (A/2) = ±

A:

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y = ...

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So fo...

Q: Let 8 be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such t...

A: We have to find g(6) 

Q: What integration technique can be used to integrate: sec3 xdx Integration Formulas O Trigonometric S...

A: Integration of a function can be done using various methode such as trigonometric substitution, appl...

Q: Find the absolute maxima and minima of the function on D, where D is the closed triangular region wi...

A: Maxima minima

Q: The number of cups of coffee sold at Lauren's Coffee House for each week in November is shown in the...

A: Consider   

Q: 1 The range of the graph y = sinx - 2 is _____. 2 ≤ y ≤ -2 -3 ≤ y ≤ -1 0 ≤ y ≤ 2 -1 ≤ y ≤ 1

A: We know that, -1 ≤ sinx ≤ 1 for all real x  

Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at x=...

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of infle...

Q: 55. A cardboard box without a lid is to have a volume of 32,000 cm³. Find the dimensions that minimi...

A:

Q: esec-1 d.x. xVx2 – 1 1

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Q: This is a two part problem. Compute the flux of the vector field F = 2x^2y^2(k) through the surface ...

A:

Q: Write an equation for a rational function with: Vertical asymptotes at x = 1 and x 3 x-intercepts at...

A: We have to find rational function for the given condation.

Q: For the function y =f(x), it was found out that f(c) = 0 and f'(c)=5. What can be said that x-c ? cr...

A:

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that L=∫ab1+[f'(x)]2dxTherefore,L=∫011+dd...

Q: Evaluate the following integrals. Express your answer in simplest form. Box your final answer. dx 5....

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Determine the convergence or divergence of the series. (If you need to use co or -co, enter INFINITY...

A: This is sequence and series problem

Q: Write a chain rule formula for the following derivative. dw for w = f(x, y, z); x = g(r, s, t), y = ...

A:

Q: Question 8 A -tan(61) + C B 6tan( 61) + C B Ltan (61) + C D - tan

A: The given integral is sec2(6t).

Q: Q3) Find the volume of the solid generated by revolving region bounded by the curve (y-e*) & the lin...

A: Integral

Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 4 %3D k! k=0 e...

A: By using sigma notation to write the Taylor series about x=x0 for the function.ex; x0=4  

Q: 22 Choose only two: (- A) Graph the two equations and find the points in which the graphs intersect....

A: To answer the given question about the parabolas.

Q: Compute the curl and divergence of the vector field F(x, y, z) = (T 2², 2yz) . Is F conservative? If...

A:

Q: sin(10) Evaluate: lim 0→0 sin(30)

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Q: Find the slope of the line through (-1, -1) and (-1, 3). undefined -1/2 0 -4

A:

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region...

A: Here, the region is bounded by y=6sin(πx), the x-axis, y-axis, and line x=1. The areas of the region...

Q: 3. Find a fundamental matrix for the following system. Then find a solution satisfying the giving in...

A: Explanation of the answer is as follows

Q: Graph of f 5. The graph of y = f(x) on the interval 0 < x < 5 is shown above. Which of the following...

A:

Q: (b) Suppose $2,100 is borrowed and the interest is compounded continuously. If A(E) is the amount du...

A:

Q: using laplare definstui fud

A: Find the Laplace transform

Q: What is the derivative of y = 34? a. y (4)(3**) b. y = 4x3 c. y = (4)(3*) In(3) d. y' = In(4x) + 34*...

A: We can answer all three subparts as below.

Q: Σ n K. n=1 e

A: According to question,Given series,∑n =1∞ nen2

Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut u=9πx2Differentiatedu=9π(2x)dxdu=18πxdxdu18π=xdxThereforeI=∫xcos9πx2dxI=∫cos...

Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm2/min...

A: Given :radius of spherical ball is increasing at a rate of 2cm/minso, drdt=2cm/min

Q: Question 22 Find all the first order partial derivatives for the following function. f(x, y) = 9x - ...

A:

Q: Use the definition of the derivative to find the slope of the tangent line to the curve y= 3x^2 - 9x...

A: We have to find the equation of the tangent

Q: Case 3: non-repeate quadratic factor (x²-x-21) Example 1: S 2x3-x2+8x-4

A: Given

Q: (x – y)² = 2ax, find the y'if a is a constant x+y a. a-x-y a-x-y b. x+y x+y+a C. x-y x-y-a d. x-y

A: Differentiating the expression with respect to x

Q: Example 19: (a) If x +y = 25, find dy/dx. (b) Find an equation of the tangent to the circle x +y = 2...

A: As asked we can find the necessary answers as below