Let T be a linear transformation from M, , into M, , such that 2,2 1 -1 0 2 0 0 1 1 Find

Q: Determine whether the vector field F(x, y, z) = x'5 i + y'5 j + z!5 k is free of sources and sinks.…

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Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

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Q: If a rock is thrown into the air on small planet with a velocity of 30 m/s, its height (in meters)…

A: Given;  y=30t-4.9t2

Q: . Find an equation for the surface area of the rectangular box. =(x, y) dy = . If the surface area…

A: We will solve the surface area problem.

Q: Determine whether the series converges. 1 k+11 The series

A: The given series,    ∑k=1∞1k+11

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the limit. If you use L'Hopitals Rule, make sure to justify why you can use it. f(x) 40 g(x)…

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Q: 6 Find the derivative of: 9/x

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Q: Write the equation of a sine or cosine function to describe the graph.

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

Q: 2x-5y ≥10 y-axis 4 3 2 1 -54-3-2-1 1 2 3 4 5 6 6 5 N -3 -4 -5 -6 x-axis

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Q: x dx 2 /9 – 4x²

A: Using integration

Q: Evaluate the integral of the following using Miscellaneous Substitution dx 1+ X

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Q: H.W: Which of the sequences {a,„} converge and which diverge: 7 1. a, = 2+ (0.1)" 2. а, n

A: A sequence &lt;an&gt; is converges if limn→∞ an is finite and exists.

Q: In the integration What is the value of u? xV1-4in?x a. u= 4ln² x In x b. u = 2 c. u = In x? d. u =…

A: The integration of the integral is  1/[x sqrt(1-4ln2x) ].

Q: Consider the curve parameterized by x 3t2 3 and y 2t°. Find equations for all tangent lines to this…

A: Here we have to find the equation of tangent line.

Q: 1. Find parametric equation for the line through the point P(3,-4,-1) parallel to the vector v…

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Q: F(4) = [, * G&+2) dt (3t +2) dt

A: Consider  F(x)=∫2x+2(3t+2)dt

Q: Evaluate the definite integral. (Use symbolic notation and fractions where needed.) dx 2x

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Q: y? = x and y2 = 2 – x %3D

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Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1

Q: Evaluate both integrals of the Divergence Theorem for the following vector field and region. Check…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + t°j dt

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Q: Exercise (2) - Solve using paper solution. d²y dy 2- - y + x = 0 dx² dx Solve using…

A: Find your answer below

Q: The curve r(0) = cos(60) is sketched below for 0 ≤0 ≤ 2π. Determine the exact area enclosed by one…

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Q: Apply differentiation rules (PRODUCT RULE) to find the equation of the line tangent to the graph of:…

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Q: Find the limit. If you L'Hopitals Rule, make sure to justify why you can use i use lim 2?e

A: We have to find the limit.

Q: A2 (II)An investment of I grew to a value of £1648.72 after 10 years with continuous compounding at…

A: Find I.

Q: H.W: which series converge and which diverge, and if a series converge find its sum: 1. E(zr n+1 3…

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Q: dx 6x + x2

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Q: 1

A: In game theory , the battle of the sexes ( BoS ) is a two player coordination game that also…

Q: H.W: vectors u =-2i + 4 j – v5k and v = 2i – 4 j + /5k , find: 1. the vector proj,u 2. the scalar…

A: Given  u=-2i+4j-5k &amp; v=2i-4j+5k

Q: Determine a, and as for each arithmetic sequence. See Examples 3 and 4. 29,. 24. -3, -7, -11,... 25.…

A: Since, the student has mentioned to solve only question number 24, so we are solving accordingly…

Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: 1. (Profit) What is the impact of decreasing/increasing radius kettle (m) with regarding to heat…

A: In the case of kettle of radius m case 1. If we increase the radius of kettle then base of kettle…

Q: Suppose we wish to find the integral of x dx/(1+x^4), the first step to solve this is by

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Q: 10. Find the position function s(t) given acceleration a(t)= 2t if v(2) = 0 and s(2)=1.

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Q: Use local linear approximation to estimate (31.62)4.

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Q: calculate the flux of the vector field through the given surface F = zi + (y −1)j + 5xk, and S is…

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Q: 7) Determine the total area bounded between the function y = 1 – x between 1 and 1. -

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Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. C:…

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Q: ydy V2y-1

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Q: Find f+ g, f- g, fg, and fig and their domains. F(x) = V15 - 2, g(x) = Vx+1 Find (F+ g)(x). Find the…

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Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

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Q: Find the arc length L of the graph of r(t). r(t) = 12 cos(t)i+ 12 sin(t)j + tk, 0<t< 2n L= 75.66

A: arc length

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

Q: Find absolute maximum & absolute minimum f define on C0, 2]

A: maxima minima

Q: [6x? arcsin(x)]dx

A: