A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = (4 cost)j + (9 sint) k. Find the minimum value of || r' ||.

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Q: The marketing research department of a computer company used a large city to test market the firm's…

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

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A: We have to find the required plane

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A: ddx(5x6ln2(x))We know that…

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A: Follow the procedure given below.

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A: We can solve this as follows:

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A: Follow the procedure given below.

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A: Here we have to solve the differential equation.

Q: ii) If there is a second eigenvalue (the second-smallest), give a basis of eigenvectors associated…

A: You have asked question (2) According to question,Given Matrix,A = 3006-306-63Eigen Values = 3, -3

Q: the complex number 6√3+6i in polar form* 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

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Q: c. Given f(x) = 2x - 3, g(x) = -4x² +9, h(x) = 4x² - 12x +9; find f(x)* g(x) 2. h(x)/ f(x) 3.…

A: Given, f(x) =(2x-3) g(x) = -4x2+9 = 9-4x2 = (3)2-(2x)2 = (3-2x)(3+2x)  h(x) = 4x2-12x+9 =…

Q: f 2³x dx = O 0 23x In 2 + C ○ 23x+1 + C 3x+1 23x In 8 0 23x ln 2 O + C + C

A: To evaluate: I=∫23xdx

Q: Find f'(0) if f(x) = = ad-bc d² ad+bc d² bc-ad d² ad-bc (c+d)² ax+b ca+d; a, b, c, d constant

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Q: The demand function for a product is given by P(x) = 80 -0.018x, where x is the number of units of…

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Q: If 5 5 f(x) dx = 4 and 2 Š² f(x) dx + O -2 O 10 O 2 0 0 4 g(x)dx? g(x)dx = 6, what is

A: Given

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Q: sec² x 0 1+tanx If sh -TT/2 -TT/4 TT/3 TT/6 O dx In 2, then what is the value of k? =

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Q: S(x + ex+1) dx 0 2. Sx5¹2 (x³ + x² - 7) dx 0 2x + 1 3. dx 2 0 e

A: Topic = Integration

Q: dw 3. If w = f(x, y, z), g(x, y) = C₁, h(x, z) = C₂ find: dx constants. c1& c2 are

A:

Q: 1 Evaluate the integral: S√72+6 dx O 2√7x+6+C O 7 2√7x+6 +C ○ // √√7x + 6 + C 1 0- + C 3 7(7x+6) 2

A: use substitution method for solving the integral.

Q: Homework) read the following mathematical steps of finding sum of series. Σ 2n = 1+2+4+8+16+ ....…

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Q: B)Evaluate the integrals: i) f/2 inzerdrde " 0 ii) f/25/2 sinx 2² siny dz dy dx. π/2

A: B.1. According to question,Given Integral,Let I = ∫0π2∫0sin 2θr dr dθ

Q: Evaluate the integral. 2 Ỉ -1 7t sec ¯¹t dt 2/√√3 2 7t sec¹t dt =

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Q: If f³ f (x) dx = 6 and ſ ƒ(x)dx = 4, then ſ5 (3 + 2ƒ(x))dx : = 35 10 23 20

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Q: Evaluate 3+x lim,¬4¹ (x-4)(x+2) 01 0 0 8-8 O +∞

A: The given limit is: limx→4+3+xx-4x+2

Q: Proceed as in this example to find the solution of the given initial-value problem. Evaluate the…

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Q: Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x² + y²…

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Q: Question -3x-13 Given that s(x) = find (s-¹)'(8) using the I x+8 Inverse Function Theorem. Note that…

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Q: 2. Which of the following sets of ordered pairs could be part of a linear function? F II (0, 1), (3,…

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Q: Q3A)Find normal line and parallel plane to the function f(x, y, z)=x²y²z²-4 At point (1,-1,2).

A: To find normal line and parallel plane to the function fx, y, z=x2y2z2-4 at point 1, -1, 2.

Q: Find the critical numbers and any local maximum and minimum points for the function ex f(x) = 2x…

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Q: Calculus I In the exercise f(x)= cos x + sin x; [0,2pi], find the following 1.) Search for…

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Q: Find the general solutions of the system. 7-9 0 x' = + 1 13 0 x 1 3 10 x(t) =

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Q: Integrate the following: 1. fxsinxdx 2. fæcos2xdx 3. fe sinxdx

A: The given integrals are' 1) xsinx 2)xcos2x 3)exsinx.  Repost the next parts.

Q: At which value of x is the function whose graph is shown below differentiable? 8 N 4 -2 0 2 4 6 -8…

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Q: Determine the direction angles for the line with parametric equations x = 5 + 2t, y = 12 - 8t, and z…

A: Direction angle

Q: On which of the following interval is f(x) S O (0, +∞0) ○ (2, +∞) O [2, +∞0) 0 (-∞, +∞0) 1 x-2…

A: We will the fact that root value should be positive.

Q: Evaluate the following integral. 48x² S dx (x-15)(x+5)²

A: Solution of given question is written in below steps.

Q: Use logarithmic differentiation to find y = x³ (5x + 3)¹ (2x - 1)5 dy dx given

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Q: Asymptotic to x= 0, x=5 and y=0

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Q: 8 (Refer to the drawing in #7) Find all vertices adjacent to v5. O V3 and vi V2 V1, V2, and v3

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Q: y = 2 sin(x), y = ex, x = 0, X = K|N 2

A: The region bounded by the curves,  y=2 sin(x), y=ex, x=0, x=π2

Q: Q2A)Matrix A = 4 ,find Eigen values of A².

A: Solve by matirx

Q: Assume that f is continuous on the set of real numbers. Find a and b given that b 3 [ f(x) dx - f₁…

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Q: Determine whether​ Rolle's theorem applies to the function shown below on the given interval. If​…

A: This question can be solved using the concept of Rolle's Theorem.