Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

Q: Consider following ODES: 1)4y" +12y' +13y=0,2) 2y″ +7y' + 5y = 0 a) Find characteristic equation and…

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Q: Find Vectors and Perform Vector Operations in R³ Let à = (3, 2, 2). Find a unit vector in the…

A: Given query is to find the unit vector.

Q: 4. y" -10y +34y = -cos3x

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Q: Evaluate a multi-variable function Let f(x, y) = √√150 - 2x² – 4y², and evaluate f(1, 0). Please…

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Q: Consider the ellipse foci? (x-5)² 256 + (y-7)² = 1. From any point on the ellipse, what is the sum…

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Q: Find all solutions of the equation in the interval [0, 21). √3 csc0-2=0 Write your answer in radians…

A: Topic = Trigonometry

Q: 4. 5 сos(x-3) dx

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Q: The following integral represents the volume of a solid of revolution. Describe the solid. =[^y₁ The…

A: Given :- Volume of solid=π∫04ydy

Q: Compute the surface area of revolution of y S I 4x + 3 about the x-axis over the interval [0, 5].

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  the given interval…

Q: Question 26 Find the second derivative (y") of the given function: y = e² sin z *)(2(- sin x)) e²…

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Q: 018 Find the area of the region bounded by the polar curve r = 2e-0 as well as the rays 0 = 0 and 0…

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Q: boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on…

A: let x = horizontal distance from bow of the boat to dock  let y = height of dock  = 1 m = costant…

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A: Recall: Volume of sphere, V=43πr3

Q: I need the P prime and Q prime of 1 and 6 P'(1)= Q'(1)= P'(6)= Q'(6)=

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Q: Find the differential of the function f(x, y) = x√y at the point (2, 7) using Az = 0.3 and Ay = 0.15…

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Q: - Find the area of a parallelogram formed by the vectors PQ and PR, where P = ( − 4, – 4, — 6), Q =…

A: See the details solution in below

Q: 6x g(x) = -5x8 + (a) | 19 (1) a (b) 1 g(a) (c) g(√a)

A: Given query is to perform indicated function operations.

Q: Scientists can determine the age of ancient objects by the method of radiocarbon dating. The…

A: given half life thalf life = 5730 years      law of decay x = x0e-ktk = constant x = radioactivity…

Q: Tutorial Exercise Find the derivative of the function. HINT [See Example 1(b).] h(x) In[(-3x + 7)(x…

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Q: If f(x) = 2x² - 3x + 6, find f'(5). Use this to find the equation of the tangent line to the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 5. Let m be a constant. For x ≥ 0, the line y = ma divides the region enclosed between y = 2x - ²…

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Q: Given: y = 5 (cosh log )², find y' (cosh² O g = =|sinh 2 log = ]5 sh®log }} O 5 O ý =−}(m& )[sinh 2…

A: The objective of the question is determine the derivative of the given function and choose the…

Q: 8 1. r = sin 20 2. r = cos 20 3. r = sin 40 4. r = cos 40 5. r = sin 30 6. rcos 30

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Q: Find the average rate of change of f(x) = 4x² - 6 on the interval [1, a]. Your answer will be an…

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Q: The expression sec² x tan³ x √tan² x+16 Otrigonometric substitution O algebraic substitution O…

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Q: The stopping distance for an automobile (after applying the brakes) is approximately F(s) = 1.1s +…

A: Given;- Fs=1.1s+0.054s2 ft

Q: irections: Consider the following function f(x). se the logarithmic laws to rewrite this function in…

A: Given query is to expand the logarithmic expression and find the values of coefficient.

Q: e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we…

A: Topic:- application of derivatives

Q: d csc 0 if tan 0 = 0 = and terminates in QII. Answer exactly. 15 Preview TIP Enter your answer as a…

A: Topic:- trigonometry ratios

Q: 2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the…

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Q: Differentiate y = ex+2 +9.

A: Given function is y=ex+2+9 We need to find the first derivative of the given function.

Q: Given the position function s(t) = 2+³ - 2 +² - 60++ 3₂ where it is in seconds and s is in ft, Find…

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Q: 23-24 Find the local maximum and minimum values of f using both the First and Second Derivative…

A: To find the local maximum and minimum values of f by using both the First and Second Derivative…

Q: Find the solutions of the following IVPS or DE. a. y" — 4y' + 4y = e²x, b. y" - 2y = e2²x +3, y(0) =…

A: See the details solution in below

Q: The volume of a cube with sides of length s is given by V = s³. Find the rate of change of the…

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Q: Solve (√x+x)=√y+y Select one: O a. y (c(1+√x) + 1)² O b. y = (c(1+√x)-1)² O cy=(-c(1 + √x) + 1)² O…

A: The given equation is; [sqrt(x)+x]dy/dx=sqrt(y)+y.

Q: 16² - 15 $+

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Q: 12 -8 I 0 Challenge #6 4 Plot a parabola through the points. When you finish, press "Check My Work".…

A: We have to plot the parabola from the given points

Q: The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x)=F(x)G(x) and…

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Q: Estimate using the linearization L(x) of f(x)=√√ at a = at a = 49. (Use decimal notation. Give your…

A: Given that , fx=1x Estimate 152 using the linearization Lx of fx at a=49.

Q: 29. Sketch a graph of a function f that satisfies the following conditions: 1. dom(f) = [-3, 3]. 2.…

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Q: Determine the derivative of ln(csc) CSC I POMOSOME CSC I O - cot a Ocot z

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Q: (a) d (√1+x²)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. 2. y"" +3y" +4y +12y = 8cos2x - 16sin2x y" - y'= -2(1+x) +4e* -6e-* +96e³x

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Find the area of the region bounded by the curves y = xe -0.4x Area = x = 5, and y = 0. >

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Q: Differentiate. h(w) (w5+ 8w^) (w-4-w-6)

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Q: Find the limit. 3 - 3 tan(x) lim x→→/4 sin(x) - cos(x)

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Q: 3. a) For what values of p is the integral cl sin b) In th x(In x)P da convergent?

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the solution of 25+1 di +T=80e-0.04² Select one: O a. T = (3.2tc)e-0.04t O b. T = (3.2t + c)e…

A: Here we have to solve the differential equation.