Express the vector 4u + 5w in the form v = v,i+v½j+V3k if u = (3, - 2, 5) and w = (- 4, 5, – 4). 4u + 5w = (Di+ O (Simplify your answer.) i+Ok

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

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A: We know that f'(x) = lim∆x→0fx+∆x - fx∆x

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A: Solving the problem by finding the value of the derivative.

Q: Please clarify the answers.

A:

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A: we need to know that limx→∞(x)=∞ and limx→∞x2=∞and∞=∞

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A: We have to solve the differential equation.

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A:

Q: Find the second derivative of x² y² + xe = 2 sin y

A: Solution is given below:

Q: dx 4–3x²

A: integration

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A:

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A: Here we have to check the concavity of the graph.

Q: - (x - 2y) dy + (5x² - 5y³) dx = 0 %3D

A:

Q: dy Solve of y = e2-3+18 In(e2²-30+18 da A. y' e2z²-32+18 (8x3 – 18z² + 85x – 57) B. y' e2a2-3a+18…

A:

Q: 3) Find the area of the region bounded by x? = y and y = 1. a. 1/3 sq.units b. 2/3 sq.units c. 4/3…

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Q: at is the absolute maximum value of = x - 3x? on the e function f(x) erval [-2,4] ? а. —20 о b. 16

A:

Q: Find the slope of the line tangent to the conic section 25 (х-2)2 (y-6)2 = 1 at (2,10). 16

A:

Q: Please do help me with this calculus questions. Please. I need the correct letter of the answer and…

A:

Q: 9. Determine whether the given integral is convergent or divergent: 1 dx? (4-x)5 a. convergent b.…

A: integration

Q: Hey sorry but I just want to confirm. What's the minimal cost of painting?

A: Given problem:- A container in the shape of a (right) cylindrical can with an open top of volume 8π…

Q: 2x Show that y = e²* sin 3x satisfies the equation y"-4y'+13y=0.

A:

Q: How did you get the volume of the hole and the ball? Referring to 4/3pi in the beginning

A: We know volume of a sphere of radius r=43πr3 cubic unit

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: The given function is: f(x)=x5+4x3+x, a=4f(4)=45+4(43)+4=1284f'(x)=5x4+12x2+1,…

Q: 1) Š(-1)"- n² 2" n=1 a) Show that the series is convergent.

A: We have to show that the series is convergent.

Q: 1. Solve the initial value problem 2 = x? – 1, y(3) = 7. dx

A: According to our guidelines we are supposed to answer only the first question if you want any…

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A: Question - 1(a) Given: y=53y=x3 Formulas used: The area bounded by the curves f(x) and g(x) is given…

Q: Can you please type it

A: Answer is given in next step.

Q: Choose the correct graph for y = cos x with the domain indicated: y= cos x, -2Asx<

A: Given, y= cos x -2pi&lt;=x=0

Q: what is b? it is the same question as a, so what is the convergence of B?

A: We can solve this as follows:

Q: 3 12х (a) 2 x2-1)2 dx 2 (x2-1)2

A:

Q: how is the irrational zero found?

A:

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: We need to solve differentiation problem.

Q: Evaluate the difference quotient for 7x+1. Az) - f(x) = 2 7/2 7 O 1/2 O O

A: Here we have to find the quotient difference of a function.

Q: Determine the value of lim,00 7²+5 a +3r+7

A:

Q: Checking using Second Derivative Test

A: From the secon derivative test, if the value of second derivative at the critical point turns out to…

Q: Determine whether the function has a limiting value. Find the limiting value if it exists.  f(x) =…

A:

Q: 8x2 – x + 8 x(x² + 4) G) + 1 2 In x + 6 In (x² + 4) – ; Arctan () + 4 In x + 3 In (x² + 4) – ;…

A: Topic:- application of integration

Q: 3) solve: y'-Hef't 44=HC032t; y0)=2, qla)== using Laplace treensform |

A:

Q: What are intervals of concavity of the function f(x) = 2x - 6x² – 3 ? Concave upward on (1, o) and…

A:

Q: Express the circle specified by x = 2 cos(0) y = 1+ 2 sin(0) in Cartesian coordinates and find the…

A: Given:x=2cosθ and y=1+2 sinθWe need to express the circle in cartesian coordinates.

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A: We have to find the velocity function, displacement and distance.

Q: (1) If x=t*2 +1and y= t*3, then the second 3 (4t) Option 1

A:

Q: can i have handwritten solution, thanks!

A: We can solve this as follows:

Q: Directions: Read carefully and solve for what is asked in each problem. ds 1. Given the velocity v =…

A:

Q: Which of the following statements is true for the function f whose derivative is f'(x) = (x + 2)e-*…

A: Here we have to find the intervals where the function is increasing and decreasing.

Q: 6. Verify each of the following identities: cosx (a) 1-sinx = secx + tanx (b) 2sec²x + 1+sin 1-sinx…

A: As you have asked for question d only. So I am solving that only. Thank you.   sec(x)*cos(x)=1…

Q: What are the local extreme values of the function f(x) = x - 3x² + 2?

A:

Q: (iii) Find the angle between the vectors. a = 8i – j+ 4k, b= 4j+ 2k (iv) Find the volume of the…

A: Given a=8i-j+4k, b=4j+2kTo find angle between two vectors:

Q: find the derivative of y=4x^2+4x+1

A:

Q: Please do help me with this calculus questions. Please. I need the correct letter of the answer and…

A: Here is the graph of the two parabolas. Green area is the intersection of two graphs.

Q: All exponential functions can be written in many forms. Write the function f(t) = 620e0.35t in the…

A: We have to transform the given function in given form function.