Let a = < 2, 4, 5 > . Find a unit vector in the direction of a

Q: Vector-valued functions (VVF) r(t) = VVF Point P t value (for point A) 1 t²i + √√4 − t j + √√t+1k…

A: Answers: 1. The domain of a vector-valued function consists of real numbers. The domain can be all…

Q: Evaluate the following integrals using partial fraction decomposition, when applicable

A: 2x2​+3x−3ln(x)​+328ln(x−3)​Explanation:

Q: 2. Use the method of shells to calculate the volume that is created when the following area is…

A: ​The required volume is, V=368π​ unit3​Explanation:Step 1:​Region is bounded by…

Q: Find the slope of the tangent line to the parametric curve x= t³ + 4t at the | y = t² + 3t point t =…

A: m= -253/52Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Given 6 = 41 - 2j and d = -101 + 73, find 16+d| and |b|+|d|.

A: Given b→=4i→−2j→ and d→=−10i→+7j→.To find : |b→+d→|,|b→|+|d→|

Q: Given f(x,y,z) = x²y³z+ye -√4-x², find the first order partial derivatives f₁, f, f

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Q: ← The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity…

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Q: Find the exact value step by step of each expression.

A: The final answer is given by:(i) csc−12​=4π​ (ii)tanθ=5​2​=525​​ (iii)cos(2sin−1135​)=169119​…

Q: Find the area of the region under the graph of the function f on the interval [2,7]. f(x) = 7ex - x

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Q: Find the curve's unit tangent vector. r(t) (2 cos ³)+(2 sin ³1) k. Find the curve's unit tangent…

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Q: Use the linear approximation to estimate (3.03)³ (1.03)³ ≈

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Q: Consider the function f(x) = 1. Find the first derivative of f(x) with respect to x. 2. Determine…

A: In this query, we tackle differentiation. We focus on the function f(x) = , exploring its derivative…

Q: On what interval(s) is the function f(x) = x - 4x³ both decreasing and concave up? (Enter your…

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Q: Answer 38,39,41Show your work

A: For answers, please refer below  Explanation:

Q: can you solve this question for me please

A: The objective of this question is to determine whether each of the given integrals is proper,…

Q: let f(x) = In (1+x). find second degree taylors polynomial centered at x=1 for f(x): f" T₂ (x) = f…

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Q: 2. Let f(x) = cx + In (cos (x)). For what value of c is f' (#)

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Q: a) Find an equation of the tangent line, at the designated point, to each of the following: i) f(x)…

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Q: Let f(x, y, z) = x4y²+ z² and x = = st³, y = s²t³, and z = st. (a) Calculate the primary derivatives…

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Q: Suppose that you are estimating √8 using the fourth Taylor polynomial for √x at x=7. Use Taylor's…

A: The objective of this question is to estimate the square root of 8 using the fourth Taylor…

Q: Calculus 1 Question. Please help   Thank you

A: Ans : dxdy​=6cos6xExplanation:Explanation:

Q: 3) Evaluate the integral 00 a) √2° 1 x√√x²-4 dx b) S√ dx -1 x2-2x Π 4 xsinx c) Số cos3x dx

A: 3.a)

Q: Snacks Movies 10% 18% Video Games Candles 36% Manga 20% 3 Mia received $150 for her birthday. How…

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Q: Rewrite the following iterated integral in the order dy dx dz: f(x, y, z) dz dy dx.

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Q: x = −1 + cos(t), y = −2+ sin(t), 0 ≤t<2π . Sketch a graph of 5 4 3 -5-4-3-2-1 2 1 -1 -2 -3 -4 -5+ 55…

A: Orientation of the graph is Counterclockwise.Explanation:

Q: Consider the function f(x) = 2√√x+4 on the interval [2,6]. (A) Find the average or mean slope of the…

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Q: 4 3 2 -5-4-3-2-1 1 2 3 4 5 3 The function graphed above is: Increasing on the interval(s) Decreasing…

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Q: Website Profit The latest demand equation for your gaming website, www.mudbeast.net, is given by…

A: the log-on fee should be $1.15.Thus, the largest possible monthly profit is $321.25.Explanation:Step…

Q: Sketch a graph of x = = 2t+ 3, y = t + 3. S 3 1 2 3 4 5 -1 -5-4-3-2-1 2 1 -2 -3 45 -4 Clear All…

A: The graph is provided below. The blue line is for y = t + 3 and the red line is for x = 2t + 3 Just…

Q: Cal math help please

A: 1. ∫x2+17x+2​dx=27​ln∣x2+1∣+2arctan(x)+C (or)                          =27​ln∣x2+1∣+2tan−1(x)+C 2.…

Q: 3. Use the method of shells to calculate the volume that is created when the following area is…

A: The exact volume is 92π(sin3−3cos3​ which is approximately equal to 2.17.Explanation:Steps and…

Q: Q7 Continuity 1 Point Let f(x) = x - 1 if x 1 x22x3 - 2x if x 1 Find the value of c for which f is…

A: for c=49​  f(x) is continuous Explanation:Step 1:Step 2: Step 3: Step 4:

Q: For the function f(x) = 4+ 12x² − x³, find the local extrema. Then, classify the local extrema using…

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Q: Find the value of the constant C for which the integral converges. Evaluate the integral for this…

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Q: Let f(x)=xex. (Round all answers to four decimal places, if necessary.) (a) Find the interval(s)…

A: The given function is As we knowThe function concaves up when The function concaves down when The…

Q: Verify that the following functions are inverses of each other. Clearly show the proofs! f(x)=2e1x+4…

A: f(x) and g(x) are inverse of each other Explanation:

Q: Given cot(y) = x, what is dy/dx?

A: dxdy​=−1+x21​Explanation:

Q: If z = tan (金) and x = u² + v² and y = u² – v², find the - following partial derivatives using the…

A: Formula for the total partial derivative is given as follows

Q: Complete the parametric equations of the line through the point (-6,1,-3) and perpendicular to the…

A: Point: (-6,1,-3)Plane: 6x-2y+2z=5

Q: A. Compute the gradient of f. vf= i+ Note: Your answers should be expressions of x and y; e.g.…

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Q: Question 2 The graphs of a function f and its derivative f' are shown. Identify each curve and…

A: We have graphs of f and f'We have to identify curve of f and f'

Q: Find к for the space curve K(t)=☐ (Type an exact answer, using radicals as needed.)

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Q: 7) Use sun and difference formula to verify the identity cos(A+B) cos(A-B) = cos2A + cos2B-1 A-B) =…

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Q: Find SS 2 2 dA over the region R = √(x0) /^< x < 4, 0 <y ≤5 } by identifying it as the volume of the…

A: The volume of the solid over the Region R with a constant height of 2 is 40 cubic…

Q: Find the smallest positive value for for which the tangent line to the curve r = 8 = Question Help:…

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Q: Find all the values of x such that the given series would converge. n=1 (x-6)" 6n The series is…

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Q: A) an = 2n+1 B) an = 5n+8n 7n

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Q: Given √,³ 0-12 f(x)dx = 8 and g(x)dx=-4, what is -4 4 12 √,³ (g(x) − f(x)]dx?

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Q: Find к for the space curve r(t) =2ti + (2a cosh (t/a))), a > 0. K(t)= (Type an exact answer, using…

A: Given:space curve- To find:

Q: For which of the points on the graph of the function f(x) shown below is f(x)0? 1. C 2. D 3.…

A: For Point Athe Y axis for point a is positive therefore,f(x) &gt; 0The slope of the tangent line at…