Given the acceleration, initial velocity and initial position, find the position function r(t). a(t) = (6t², 2t), v(0) = (1, 3), r(0) = r(0) = (0, 2)

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

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Q: y = tan 2x 1-cot 2x

A: Given,            y=tan2x1-cot2xTo find : Find the derivative of the given function.

Q: a. f(x) = on [-1,4] 1²+2 b. f(x) = I√4-1² on [−1,2] c. f(x) = 2 sec r - tan r on [0,1]

A: At the  extremum of a function f(x), the first derivative is zero.

Q: Question Use the binomial series expansion, 1 for the function f(x) (1 - 2x)² If necessary, round…

A: Let's find.

Q: Activity 2: Solve each function below the letters and decode the unknown word in each number. Once…

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Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Use AXYZ, as needed, to complete the given parts. Part 1: Z 15 cm Part 2: Part 3: Part 4: Y 7 cm X h…

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: Evaluate the integral order of integration. NOTE: Enter the exact answer. I fe e² dx dy= = e² dx dy…

A: Given:         ∫06∫y23ex2dxdy  Reversing the order of integration.       y2≤x≤3    y≤2x≤6…

Q: y = 2-ex 3x-1

A: We know that differential power rule is given as - d(xn)/dx = nxn-1.   Here i attached the solution…

Q: Part 2: Exponential Growth and Decay and Logistic Growth Model (3) Suppose an experiment was…

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Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

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Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: to express the integrals as limits of [ f(x) dx (b) [f(x) dx

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Q: The graph of a function f is shown below. 6 -1 -2 1 Suppose the function g is defined as g(x) Fill…

A: In this question , we can find the limits of the function. Check when 'x' approaches to 'a' , the…

Q: A company can buy a machine that is expected to increase the company's net income by $15,000 each…

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Q: Find the Laplace Transformation of y" +3y + 2y - 4ex when y (0) = 0, y′ (0) = 3 OY (s) 2s+1…

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Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

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Q: Consider a triangle ABC like the one below. Suppose that C= 123°, a= 15, and b=37. (The figure is…

A: The Cosine rule; a2=b2+c2-2bccosAb2=a2+c2-2accosBc2=b2+a2-2abcosC Given: C=123°, a=15, b=37

Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4.

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Q: A cat darts around a room chasing a ball. The cat first travels along the vector (-1,2) and then…

A: Given ,  A cat darts around a room chasing a ball. the cat first travels along the vector < -1, 2…

Q: Answer B True False The derivative of the function y=x²log (1-x²) is x² y=2xlog (1 - xảy - 2 1-x

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Q: Prove sinxtanx + sinx tanx 1 cosx is an identity.

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Q: 5-39+370=?

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Q: Find a3 w дх ду дz if w — exyz = 0.

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Q: How to determine whether the function is continuous or not at a given point x = a ? x ≤ 1 (3x5 - 1…

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Q: C. Find the angle coterminous to the given angle that has the opposite sign. бл 1. - 7 2.-258°

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Q: y = 3x-2\4 4x-5

A: WE use the properties of logarithm to find the derivative

Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all ^~^ints.…

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Q: 7) Relative to an origin O, the position vectors of the points A and B are given by OA P (-) and OB=…

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Q: Evaluate the iterated integral. [[ (x + y) dx dy

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Q: 0 3. Evaluate the definite integrals: (a) CS Scanned with CamScanner² (x² – 3x) dx (b) 5 1 √I -d.x

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Q: 0 if t 5 Find the Laplace transform, F(s) of f(t) F(s) = ķ

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Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

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Q: x +4 x² + 2x + 5 dr

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Q: Given: y = cosh cosh (ex²)

A: Formulas:ddx cos hx =sin hxddx ex =exddx xn = n xn-1

Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: Determine whether the improper integral diverges or converges. 00 x²ex dx 0 O converges O diverges…

A: Given query is to find integral converges or diverges.

Q: Consider a triangle ABC like the one below. Suppose that b=58, c=34, and B= 108°. (The figure is not…

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Q: Find the present value of a $8,000 annual income stream if it is invested immediately as it is…

A: Compound continuously A=Pe^(rt)

Q: 16. (a) 6 dx (b) -10 (c) √² 2) |x - 2| dx (d) 17. In each part, evaluate the integral, given that…

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Q: dx √1+√√x |

A: Given,  ∫dx1+x

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-l is convergent or…

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Q: 4. Find the antiderivative of 1-t4 = CS the t that satisfies the given condition R(1) = 4

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Q: 1 A tank with a capacity of 400 gal initially contains 100 gal of water with 50 lb of salt dissolved…

A: 100gal=Initial amount of water in 400gal tank50lb=Initial amount of salt in the tank1lbgal=salt…

Q: Je-2x sin 2x dx

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Q: * Find the fourth derivative 1 y=x²- HJXJ

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Q: 7. The height (metres) of a bouncing ball can be modeled by the function h(t) = 2sin4t + 2 over the…

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