ctivity 2. Answer the following problems. 1. A child is flying a kite at a height of 40 ft, that is, me of 3 ft/sec. If the string is taut, at what rate is the s the length of the string released is 5 ft? 2 A spherical snowball is being made so that its volum of 8ft /min/ Find the rate at which the radius is inca is 4t in diameter. 3. A stone is dropped into a still pond. Concentric circular radius of the disturbed region increases at the rate of 16 c area of the disturbed region increase when its radius is 4

Q: Use the areas shown in the figure below to find the following. y = f(x) Area =0.7 Area =15 a Area =2...

A:

Q: 3. A rectangle with a fixed perimeter of 64 units is rotated about one of its sides, thus sweeping o...

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

A:

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: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-6ax=0x+y=6a The small bounded region is rotating about the line x=0.

Q: Let a = ci + j and b = 8i + 15j. Find c so that the angle between a and bis Round your answers to fo...

A: To find the value of c

Q: Use the Root Test toO determine if the series (-1)" 2/n Σ CONVERGES en? (2n2 – 1)" n=1 converges or ...

A:

Q: Type the standard form of the equation. Find the standard form of the equation of the ellipse and gi...

A: The standard form of the equation of an ellipse with center (h,k) and major axis parallel to the x-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: Use the Root Test to determine if the series (-1)" 2'/m Σ en² (2n2 – 1)" | n=1 converges or diverges...

A:

Q: dy then dx sin x If y = 1+ cos x ||

A:

Q: Hew-2 Verify that Wxy Wyx fer the functions's T- R(Xsy) = Lu (2X +34) f cxッy) é^+x Luy +y Lnx 2-

A:

Q: 2 cos 0 d0 V1 – sin 0

A:

Q: Activity 2: Determine the absolute extrema of the function f(x) = x - 12x on [0, 4]. %3D Show comple...

A:

Q: x dx

A:

Q: dy If y = x. 5* then dx

A: To find the derivative of the given function.

Q: y = 6+4 Vx csc x

A: Topic = Derivative

Q: dx Evaluate f x2V4+x?

A: Given:          ∫dxx24+x2   Perform trigonometric substitution:      substitute x=2tanu→u=arctanx2  ...

Q: Find (e-*) dzdy A. 4ye-(*²+y²) B. 4xe-(2²+y²) C. 4xye-(x²+y²) D. -4xye-(a²+y²) OC OA OB None of the ...

A: Partially differentiate the function y= e-(x2+y2)  w.r.t. x and y . 

Q: ( y2 sin r dr

A:

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

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

Q: | In|V + 1| dx

A:

Q: x dx e

A: This question is based on integration by parts.

Q: Consider the power series rvn(5– 2x)" 2n + 1 Vn(5 – 2x)* n=1 a. Show that the series is conditionall...

A:

Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10...

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,  

Q: Vx - 2 dx xõ(Vx+ 1) x +

A:

Q: Find S x² sin x dx

A:

Q: A lamp is placed on the ground at a distance of 17 feet from the point at which a rocket will be lau...

A:

Q: | InlvE + 1| dx

A:

Q: 10)A doctor prescribes 300 milligrams of therapeutic drug that decays by about 10 % each hour. What ...

A:

Q: 2 cos @ dӨ . 1- sin 0

A:

Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the...

A:

Q: x2+1 - dx x4-x²+1

A:

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

A:

Q: R(t) = 2 sint-4 cost

A:

Q: 2 cos 0 de V1 – sin 0

A:

Q: V- 2 dx +1)

A:

Q: Find the linearization of f(x, y) = V1+x - y? at (4, 1), and then use it o approximate f(3.96, 1.02)...

A:

Q: Activity 3: Find and simply the result, if possible. 1 a. y = vx - b. y = x? + n + x" C. y = x² secx...

A:

Q: Consider 5 28 +2 x2 +2 sin(x)–2 -28+5x+5 f(x) = Find the behaviour of f(x) as x → 0. • If lim f(x) e...

A: Here, f(x)=5x8+2x2+2sin(x)-2-x8+5x+5

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y? = 2(x2 – ...

A:

Q: Definitions/Examples a. A = {0, 0, =,A), B = {a, 0./. = } b. Every element in set A is also an eleme...

A:

Q: Find the antiderivative, G(t), of the function g(t) = (3n²t² – t*)V3n² – t².

A: I am attaching image so that you understand each and every step.

Q: A Find 32 31¥ and 22f fer the functions tre etan (x+y) 2- 우Cx,y) x ty + cosy +y sinx. %3D

A:

Q: Evaluate using Wallis' Formula: 7 sin? x cos5 x dx

A: follow next step

Q: cos x dx – sin z V1- sin x Determine

A:

Q: a man who is standing 5 meters above a shoreline is pulling up a boat that is 12 meters away from th...

A:

Q: dx -2 3 (5-4x- х?)2

A: Let's find. 

Q: Find the area of the triangle with vertices P(1,3, –3), Q(0,0,0) and R(4,6, 1). NOTE: Enter the exac...

A: Area of triangle is half of cross product of adjecent side of traingle.