Find an interval of t-values such that c(t) = (cos t, sint) traces the lower half of the unit circle (in the counter-clockwise direction). interval = Note: Use lowercase "pi" for T. Example answer: [0, 1].

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Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt' the product directly and…

A: r1(t)=cos⁡(t)i+sin⁡(t)j+6tk,r2(t)=5i+tk Given:  ddtr1(t)⋅r2(t)=r1(t)⋅dr2dt+dr1dt⋅r2(t) and…

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: Solve the triangle. Round your answer to the nearest tenth. mZA = 37°, a = 28, с 26 mZB 109°, m2C =…

A: Given query is to solve the triangle.

Q: 3. Let f(x) = x (x² + 1)/2. (a) Evaluate fo f(x)dx using integration by parts. (b) Evaluate f f(x)dx…

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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: For f and g defined below: 15V 10 y = g(x) -10 10 15 y = f(x) -10- g(-5) is undefined. f(15) is…

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Q: Integration

A: We will solve the integral.

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: dx Half-angle Substitution cos x +sin x-1

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Q: (D² +1)y = sec x. %3D

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Q: Use the Taylor series for f(x) = Vx, centered at a = 16, to approximate the numerical value of v17.…

A: This question can be solved using the concept of Taylor series centered at a.

Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Find V x (V x F) if F(x, y, z) = 5xyj+7xyz k. %3D V × (V × F)

A: Curl vector

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Q: S etanx sec²x dx

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Q: Find the length of segment AB. Round your answer to the nearest tenth. A 51° 26° 20 mi B 15 mi 16 mi…

A: ANSWER: 16 mi SEE ATTACHMENTS

Q: Find the area lying outside r = 6 cos 0 and inside r = 3+3 cos 0. Area =

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: Determine the area of the glven reglon. y = x + sin x 3- 2- Step 1 Note that for the given reglon, x…

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Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

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Q: Consider the following. z = x2 + y2, x = 4s + 8t, y = s +t az az and as Find by using the chain…

A: Here, the given functions are: z=x2+y2, x=4s+8t, y=s+t So, z is a function of x and y and x and y…

Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: 7 For AABC, you are given m2C = 39°, mZB = 44°, a = 30ст. Find c. 17.9 cm 16 cm 19 cm 22 сm Previous

A: We will find the c.

Q: cos2x dx sinx

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Q: Use a truth table to determine whether the two statements are equivalent. (p v q) a r and p v (q A…

A: Here we have to find the truth table.

Q: Find an equation for the plane tangent to the level surface x² + y? +z = 4 at the point Po(1,1, 2).…

A: Solving

Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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Q: v F= F=

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Q: ) Find an equetionof tue tenyent line to the greph of d= In(x') at the point (l,0). Angwery8 a) y*-5…

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Q: り (2xy+y?) dx - 2x? dy = o 2) Yy dx - (メ+ 2y)? dy -0

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Q: Answer the following questions for the function f(x) = x/x? + 1 defined on the interval – 5 <x < 7.…

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Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: fF(x)dx = -9 and Si (x)dx = . 3 tind f(x)dx Given that

A: We can solve the answer using the properties of definite integral as below.

Q: Evaluate the definite integral. O e10 e10 - 1 i+ k 10 10 - 1) j+ k 1- e10 - 1 10 e10 i - e j+ 1 k 2…

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Q: 1. S 2x-6 すdx (x-7)5

A: Solution:

Q: Please

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Q: Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from…

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Q: dz Find given: dt z = ze", z = t°, y = 1+ 4t dz dt Your answer should only involve the variable t

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Q: differential cgnatuin as A. Identify the given to the dependent variable, degce z the eguati degre 3…

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Q: 5. f(x) = (3x² + x)e5x² %3D

A: Explanation of the answer is as follows

Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: A Find the area bounded by the curves, the axis and the given values of x. Sketch the graph. 1.…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…