Consider the two functions fz) = 5x +5 and g(x) = 5x² - 5. a. Determine the instantaneous rate of change of A) with respect to x at the point with x-coordinate 5. b. Determine the instantaneous rate of change of g(x) with respect to x at the point with x-coordinate 5. c. Compare these two answers.

Q: Evaluate *(x-2) dx (x-1)3

A: We can find the required answer in the following steps

Q: Find f'(x) if eſ(x) = 1 + x². f'(x) = 2x(1 + x2) f'(x) = 2x(e1+**) Option 1 Option 3 2x f'(x) = 1+x2...

A:

Q: dx Evaluate x²V4+x²

A:

Q: A dart is thrown at a number line in such a way that it always lands in the interval (0,10J. Let x r...

A:

Q: 11. Obtain the Mx and My of the area generated y = 2x +1, x + y =7 and x= 8

A: Intersection points:x+y=7, y=2x+1y=7-x, y=2x+17-x=2x+13x=6x=2 → y=5Intersection point (2, 5)Line x=8...

Q: Find the derivative of the following trigonometric functions and simplify if possible. Box your fina...

A:

Q: ха + ах — 2bx -2ab — х3 — 2ах* — 2bx? x* + ax³ – 2bx³ – 2abx² dx

A: Given integration is: ∫x2+ax-2bx-2ab-x3-2ax2-2bx2x4+ax3-2bx3-2abx2dx

Q: (c) Same direction as the vector from the point A(-1,0,4) to the point B(4,3, 3). 1 i + 2 w = k - 6.

A:

Q: dy If y = In V4x² + 5x_then dx

A:

Q: G(t), of the function g(t) = (2n?t? - t)V2n2 – t?. %3D

A:

Q: n4 +1 n=1 7(-1)3n

A:

Q: Given x+ y +z=3 and Po(2,1,0), find the following. (a) Find the equation for the tangent plane at th...

A:

Q: b) an = (-1)"/n (-1)" Vn c) an

A:

Q: Find the area bounded by y = sin²(x) and y = sin³ (x) from< xS n.

A:

Q: 9. Given f(x) =-Vx – 3 and g(x) = x² + 3x + 4, what is the domain of z(x) = f(x) – g(x)?

A: 9. The functions area given by fx = -x-3 and gx = x2+3x+4 To evaluate: The domain of the function zx...

Q: Find the truncation error of the following Maclaurin series given that it is truncated into 3 terms:...

A:

Q: "/2 cost x dx "/4 sin6 x

A:

Q: 1+cos 4x dx 1-cos 4x Evaluate

A:

Q: Evaluate the function y = - for x = 3 to x = 5 in steps of 0.5. Write the complete x+ code

A: % Matlab Code% defining the range for xx = 3:0.5:5;y = (x) ./ (x+(1./x.^2))

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k? = 0 and ...

A: Given curves are:  x2-2kx-4ky+k2=0 4x-4y+k=0 The area bounded by them is revolving about the line x=...

Q: /9-4х2 dx

A: We know, (i) ∫dxx2-a2=12alogx-ax+a+C, C is a constant.

Q: ind the antiderivative, G(t), of the function g(t) = (2n²t? – t*)v2n² – t2.

A:

Q: Va –2 -dx aㅎ (V+1)

A:

Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (х — 2) %3D 4(у + 2)...

A: Given that the area is bounded by x-22=4y+2 and y=-1.It is required to find volume generated by revo...

Q: Find the volume generated by revolving bout the line x = 3 the area bounded by (y – 2)° = -4(x – 4) ...

A:

Q: sin 3x y = 4+5 cos(2x)

A:

Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2 ...

A:

Q: Suppose a function z=f(x,y) has critical points at (-1,2) and (0,3). Furthermore, suppose at each cr...

A: Let's find. 

Q: Find the area of the shaded region. NOTE: Enter the exact answer. x = y A = 6. 27 x = y? 6

A:

Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. NOTE: Enter the exact answe...

A:

Q: y=3-x + xlnx solves y' = Inx y = solves y' = y? 1-x

A: This question is based on differential equation.

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 3ky + k² = 0 and ...

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line x=...

Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.

Q: Find the length of the arc of the curve 4y² = 9x³ from the origin to the point (2,3v2).

A: Arc length of a curve y=f(x), x∈[a,b] is given by,          L=∫ab1+y'2dx ∫xndx=xn+1n+1+C, C is a c...

Q: Find the volume of the solid generated of the area bounded by y2 = 8x and y = 2x, rotated about y = ...

A: Given:-the region bounded byy2=8x and y-2xrotating about y=4using cylindrical shell methodr=4-yh=y2-...

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A:

Q: Зх-1 13. f (x) = ;(-1,6] х2—7х-8

A:

Q: Sketch the curve f(x,y) = c together with Vf and the tangent line at the given point. Then write an ...

A: Solution is here

Q: Find the vector -4u+2w given the vectors u = -8j and w =-6i+5j. Write your answer in the form ai+bj....

A:

Q: S tan bxsec³bxdx

A:

Q: 3 2 1+ X 1 Let R be the region in the first quadrant enclosed by the graphs of y = 10e- sin x and th...

A:

Q: 4. Let p and q be variables with truth-values 0 or 1. Find logical expressions of p and q that repre...

A: We have to complete the truth table and to find the following question.

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 4(x² – ...

A:

Q: Lof the function a(t) - (2n2+2

A: We have to find the antiderivative of the given function

Q: Evaluate (2 cos x-sin x)² -dx sin x

A: We have to solve the above integrals 

Q: 4 antegrate the ff 2. (ax-6)*dx 2. (x2 +5x DISTRI BUTI VE PROP.

A:

Q: The radius of a right circular cylinder is increasing at the rate of 3 inches per ninute and the hei...

A: Given:The rate of change in radius =3 in/mThe rate of change in height =4 in/mThe radius =9 The heig...

Q: III. Show that the function is continuous on the specified interval. 11. f (x) = V3x – 5; [3,9]

A:

Q: Find the length of the arc of the curve 9y? 4x3 from the origin to the point (3,2v3).

A: Here, the given curve is: 9y2=4x3⇒y2=4x39⇒y=23x32 Now, the length of the curve on [a,b] is given by:...

Q: 出w-2 Verify that Wメy Wyx for the functionss T- f(xsy) = En (2X +34) fcxyy) = e+x Luy +y Lnx 2-

A: