dr If dt dA when r = dt Let A be the area of a circle with radius 5, find 4. r. | ||

Q: Find the area inside the curve r = 6 cos 20 and outside the curve: r = V3

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Q: Given the double intergral 3 S.³ To √²+y² Evaluate the above dy dx intergral using cartesian…

A: some of the formula of integration . ∫1x2+a2dx=ln|x+x2+a2|+C∫xndx=xn+1n+1+C

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: dr = 3, find dt dA when r = 5. dt Let A be the area of a circle with radius r. If

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Q: Plot the following quantities versus distance along the beam a) Displacement (y). b) Slope 0(x) =…

A: Note: Since you have posted multiple sub parts. As per our policy we are allowed to solve the first…

Q: Let f(x)=((4/3)?^3/2) .Calculate the arc length of the graph of f(x) over the interval [0,2]. Round…

A: Given, the function We have to calculate the arc length of the function over the interval [0, 2].…

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Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

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Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: Find dw/dt at the given value for the following functions dw Ans. dt 1) w=x+y, x=cos(t), y sin(t),…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take = 3.

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Q: Find dw/ dt at the given value for the following functions dw dt 1) w= x + y°, x= cos(t), y= sin(t),…

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Q: Find the approximate value for f(r, y) = sin(x7xy + ln(y)) at (0.03, 1.04). Take a = 3. %3D

A: We have to do two variable linear approximation here and find the required expression first.

Q: Find the arclength of the curve in the given interval. x = 3 cos? t , y= 3 cost sin t , 0 s<t <t

A: solution is written in below steps.

Q: On what interval(s) is the curve concave upward ? Answer (in interval notation)  y=integral a=0…

A: Given: y=∫0xt2t2-t+3dt

Q: dr Let A be the area of a circle with radius 7. If dt 3, find dA dt when T I 7

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Q: d'y Find for dr? y = cot(x) dy %3D dx?

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Q: Suppose that the radius r and surface area S = 4pai r2 of a sphere are differentiable functions of…

A: The relation between surface area and the radius of the sphere is as below.

Q: When the radius r of a sphere increases with time t, the change in area dA is dt Оа. 4 3 O b. dr 8n…

A: We will find the change in area with time as following.

Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: Find dy/dx implicitly and find the largest interval of the form −a &lt; y &lt; a or 0 &lt; y &lt; a…

A: tany=x Differentiating with respect to x, we get ⇒ddxtany=ddxx⇒sec2ydydx=1⇒dydx=1sec2y⇒dydx=11+tan2y…

Q: The arc length of y = 5++ from x = 1 to x : 2x (A) f 1+ (5 ++² dx +2 dx 2x (B) 2x2 (C) f1+ x2 dx 2x2…

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Q: If the area enclosed by the curve x = 4 cos³ t and y = 4 sin t (wheret e R) is A then what is A?

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Q: Suppose that the radius r and surface area S = 4πr2 of a sphere are differentiable functions of t.…

A: Given surface area of a sphere, S=4πr2, where r is radius of sphere. It is given surface area is…

Q: Find the arc length of the function f(x) 3/2 2 on the inverval 0 S x < = %3D 15 (A) (B) (C)# (D) (E)…

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Q: The integral cot(x + 1) dz is transformed into (t) dt by applying an appropriate change of variable,…

A: Firstly we assume any function related to given question

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Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 1.

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Q: Integrate f (z) = z² around the unit circle which is defined by y(t) = cos t + i sint and t E…

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Q: Find the approximate value for f(r, y) = sin(a7zy + In(y)) at (0.03, 1.04). Take a = 3.

A: We have to find the linear approximation of the given function around suitable point.

Q: ind the unit tangent, T(0), unit normal N(0), and binormal B(0), at t = 0 for the parameterized…

A: Given that: r(t)=5cost.i+5sint.j+7k

Q: mifferentiate with respect to t. y = a cos(t) + e sin(t)

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Q: Let y = sin(2x). If Aa 0.3 at a 0, use linear approximation to estimate Ay Ay = Find the percentage…

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Q: H.W H find the degree of Precition. O F(x) = X

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Q: integrate ƒ over the given region. ƒ(s, t) = es ln t over the region in the first quadrant of the…

A: The given function is fs,t=eslnt over the region in the first quadrantof the st-plane that lies…

Q: Find the first order derivative for the following: cot(e(+M)y) sin(My²) + Vx4 + Mex %3D

A: We will find  ∂T/∂x,    ∂T/∂y

Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 4.

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Q: Suppose that the radius r and area A = pai r2 of a circle are differentiable functions of t. Write…

A: Given, Radius = r Area = A= pi*r^2

Q: th² (t) В V = 2

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Q: Let f(x)= sec(x), find the linear approximation at x= pi/4 and use it to estimate sec(pi/5)

A: Given function: fx=secx At x=π4 fπ4=secπ4=2

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A: Given data:Degree of freedom  =27 Area to the right  = 0.01

Q: The graph of f(x) = sin z has horizontal tangent lines at z = Select one: O a. + kn, k E Z. O b. kn,…

A: Given: f(x)=sin x

Q: JT 9 cos' t and y 9 sin't (where t E R) is A- then what is 8. If the area enclosed by the curve x =…

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Q: dy Find dx or y' of the following functions and make any obvious simplifications: a. y = arctan(e")…

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Q: The integral that represents the length of the curve 7(t) = (t, cos (2t312), sin (2t312)), where Ost…

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Q: 1 dx Estimate J. using the Trapezoidal rule and Simpson's rule. 0 1+x² Compare results by using n=2…

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Q: The volume V of a right circular cylinder of radius r and height h is V = Tr²h. (a) How is dY…

A: Given , V=πr2h V is volume ,r is radius and h is height of  a cylinder

Q: Find the area inside the circle r = –3a sin 0 and outside the cardioid r = a(1 – sin 0), a > 0. -

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Q: When mineral deposits form a uniform coating 1 mm thick on the inside of a pipe of radius r (in mm),…

A: We have to sketch  f(r) = π r2 - 2r + 1.