Prove using elements that for any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: Va + 4 What is the domain of the following function: f(x) = %3D x- 7 0[-4, 0) O (7, 00) 0[-4, 7) U (...

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all tha...

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Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (3, 0) %D Vg(3, 0) = %3D

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Q: Use the graph of y-f(x) below to determine which of the choices could be the graph of y=f(x) Hint: M...

A: In order to graph the function y=f'(x) firstly we need to find the signs of f'(x) at various interva...

Q: Given vector u= (-3, 3) and v = (6, –2), determine the value of 4u + v in | component form.

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Q: P that is orthogonal to the vector AB. . B e distance from the point P(-3,1,9) В(-2,3, —4).

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Q: If f(x) = x' = 4x² + 10 determine the contavity when x=1. Hint: First find the second derivative O[®...

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Q: O Watch help video 4x and g(x) = 2x² Let R be the region bounded by the functions f (x) = -2x² - as ...

A: solution is given below

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx

A:   Solve for the derivative of the function using chain rule. 9. f(x)= esinx  

Q: A point starts at the location (4.5,0) and travels CCW along a circular path centered at the locatio...

A: Solution: According to question, the diagram should be like this

Q: I7 The Sind the squou in vares

A: Given query is to find the unknown numbers.

Q: Given vector V = (2, –2) , find 3v graphically by stretching the vector by its tip and then writing ...

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| = ...

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Q: A fence 20 feet tall runs parallel to a tall building at a distance of 4 ft from the building as sho...

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the po...

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given ...

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Q: draw a tree diagra w : fLx, y,z,N n and write chain rule! ニ y = f lu,v) , Z=f lu,V), N= f (u,V).

A: Here we will draw tree diagram and write chain rule,

Q: Consider the following. u = (5, 7), v = (6, 2) (a) Find the projection of u onto v. (b) Find the vec...

A: Given, u=<5,7> v=<6,2> projvu= (u.v/|v|²).v u.v= 5*6 + 7*2= 30+14= 44 |v|= √(6²+2²)= √(3...

Q: A fence 12 feet tall runs parallel to a tall building at a distance of 6 ft from the building as sho...

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Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: Airport B is 300 mi from airport A at a bearing N 50° E (see the figure). A pilot wishing to fly fro...

A: Given query is to find indicated angle.

Q: cos x х dx /sin x COS

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Q: III. Derive the following HCA 1. The unity rule: = 18 dx du dx 2. The quotient rule: xp dx

A: f(x)=xDerivative formula:f'(x)=limh→0 f(x+h)-f(x)hf'(x)=limh→0 (x+h)-(x)hf'(x)=limh→0 hhf'(x)=1ddxf(...

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+2k w = i+ 9j + 2k Find the v...

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Q: Calculus Question

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Q: Consider 12 – 2x +1 if r 1. Determine if the following functions are continuous on the interval I. ...

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Q: Use induction to prove: for any integer n 2 0, 2. 3 = 3"+1 - 1. %3D j=0 Base case 2.3 = j= n = , 3n+...

A: for any integer n≥0,∑j=0n2. 3j=3n+1-1

Q: S ds J V3s? + 1

A: To evaluate the given integral  

Q: (x – 3)2 (y – 2)? = 1 - Given the ellipse 16 36 Find the center point: List the two major vertices (...

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cub...

A: This question can be solved using the concept of maxima and minima.

Q: A 25-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away fro...

A: Question- 25-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides ...

Q: Answer the following True or False: For every continuous nonlinear function, you can find a value of...

A: To states whether true or false. For every continuous non linear function, there is a value of x tha...

Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

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Q: Find when the function is concave up and when it is concave down. (remember it is arctan not an expo...

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Q: Evaluate these limits as x approaches infinity or negative infinity- Question 1 x2 + 3x + 1 lim,m

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Q: 5. Find the general solution of the given differential equation y" + 3y" + 3y + y = 0

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Q: Given the piecewise function defined below, determine the value of f(x)da in simplest form. -2x 3 fo...

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Q: 4. D, (x-2)(2x +3) 5. D, (e")

A: We know that, Dx(ex) =ex Dx(xn) =nxn-1

Q: Give The 15T four non zero Term of Mhe Sentes aboufx= %3D

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Q: R be the region bounded by the functions f(x) = -4x2 + 10 and :) = 4x +2 as shown in the diagram bel...

A: Given query is to find the are bound by the curves.

Q: 1. Find the area of the region enclosed by loop of the curve T = cos(46 one 1.0 y

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Q: 3. Find the area of the region that lies inside both curves: r = sin 0,r = cos 0 0.8 0.6 0.4 0.2 -0....

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Q: 3. Find the slope of the tangent line to curve x=2sin2t, y = cos4t when t=-

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Q: OF(x)= - 2x3+ 84x2-72x on 7- -6x²+48 x-72=0

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Q: 5. f(x) = [(x + 5)5 – 1]4

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Q: 1> =a,-4,57is to U=2,-4,5 812.Detemmine -> onthogonal

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Q: The number of users on a website is 3200 and is growing exponentially at a rate of 70% per year. Wri...

A: This is a problem related to exponential function. Based on the general formula we will answer the q...

Q: A box with a square base and open top must have a volume of 42592 cm. We wish to find the dimensions...

A: To minimise material we have to minimize the area

Q: Graph the following on the given axis. Note there are two problems, see the back side. 1. Graph the ...

A: Draw the graph of given condition f' x>0  if x≠3f'' x>0  if x<3f'' x<0  if x>3 f has ...