Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i + 2t²j, t = 3 T(3) = X

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A: The objective is to find instantaneous velocity and speed at time t=5sec.

Q: 8. Find the area bounded by y=ex, y=x² and x=2. a. 3.1 u² b. 4.1 u² c. 5.1 u² d. 6.1 u²

A: Here we have to find the area bounded by the given curves.

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Q: ) Find f'(x) given that f(x)= 2x² + 3 x² - 5x+2

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Q: Example 5: Use double integral to find the are

A: In this question we will use basic concepts of double integration to get the required area bounded…

Q: Q6) Test the convergence of the following (n+1)(n+2) 1) Σ=1 n!

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Q: Which of the following represents the difference quotient for f(x)= -²₂ 2 x(x+h) 2 x(x+h) 2x+h…

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Q: Solutions converge to the function y =

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Q: Find the solution of the given initial value problem. πT ty' + 2y = sint, y = 3, t > 0 Y ||

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Q: You have a penny, a nickel, a dime, a toonie, and a loonie. How many different (non-zero) sums of…

A: You have penny, nickel, dime, toonie and loonie  How many different sum of money produce

Q: Evaluate the following integral. 3 5x(x - 3)dx 0

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Q: Find an implicit and an explicit solution of the given initial-value problem. (Use x for x(t).) dx =…

A: The given initial-value problem,dxdt=4x2+1, xπ4=1

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Q: Find the derivative of each of the following functions using any method. 7.) f(x) = 6cot(sin(4x))…

A: 7. fx=6cotsin4x8. fx=6sec7x29. fx=e6x2-17

Q: Let f(x, y) = x² - In (36-4x² - y²). Then the domain off can be represented by the blue region in…

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Q: Find the indicated limit if it exists. √x+4-2 a) lim X-0 X 8x³+27 b) lim x-1.5 2x + 3

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Q: 150 liters of fluid in which 20 grams of salt is dissolved. Pure water is then pumped into the tank…

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Q: lim (tan x) cos x x-2 X-

A: This question is based on limits of 0infinty indeterminate form.

Q: 16 f(x) = x² + x>0 " X (a) Find the relative extreme point (s) of f; (b) Find the point (s) of…

A: As per our guidelines we are supposed to solve only three sub parts of the problem. For the first…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Q2: Find y(2) if D.E as give 2 dy+3y=sin 2x, y(0) = 6 dx Given

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Q: To say that x + 5| ≤ 3 is the same as saying is in the closed interval [A, B] where A is: and where…

A: The objective is to find A and B.

Q: Use the graph of f to evaluate the following: 6 + f(x) 5 X 4 رها 3 N 1 1 2 4 5 The average rate of…

A: Equation of slope:  Slope =(y2-y1)/(x2-x1) The average change of the function over the given time…

Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: 2.) (cotx + tanx) ² dx

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Q: f Cos 6 x dx 2 Cos ²3x

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

Q: 2x² + 3 Find f'(x) given that f(x)= x² - 5x+2 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ -…

A: I am attaching image so that you understand each and every step.

Q: 7) lim (cotx +cscx) XIR

A: lim      cotx + cscx x -->π lim      cosx/sinx + 1/sinx x-->π lim      (1 +cosx)/sinx x-->π…

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Q: a) Graph the function f(x)=2x-5x + 3. b) Draw a tangent line to the graph at the point whose…

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Q: At what point do the following lines in R³ intersect? l₁ : (x, y, z) = (1,2,1)+ s(1,0,1), l₂ : (x,…

A: See the answer below

Q: B) Evaluate the line integral of the function P(x,y) dx + Q(x,y) dy. over the curve C where…

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Q: Find the arc length of the curve y = 2/3 (x − 1)3/2 on the interval [2,3]

A: Arc length is given by the following formula

Q: The value of n when integrating the following function using Simpson's method is: [2²/ dx h = 0.2 >

A: solution is given below

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Q: Find the solution of the given initial value problem. T ty' + 2y = sint, y = 3, t > 0 2 Y ||

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Q: Let f be the function defined as follows. y = f(x) = √5x + 5 (a) Find the differential of f. dy = X…

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Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)-0 Find y(0.1)?

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Q: Q2: Find y(2) if D.E as give dy 2+3y=sin 2x, y(0) = 6 dx Given

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Q: Solve the differential equation where y = 8 when = 0. y + 3y x + 3 = (x+3)8

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Q: 8 hp zh6 S

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Q: * Find dy/dx for the function_y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

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Q: Using the definition of derivative that incorporates the idea of limit, prove that if f and g are…

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Q: WA #

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Q: 3 3 x³ - y³ z = f(x, y) = x² + xy + y² 0 for for (x, y) = (0,0) (x, y) = (0,0)

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Q: Find the first partial derivatives of the following function. f(x,y) = 8x4y

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Q: Follow the steps below for the given function. xy5y - 8 = 0 Solve the equation for y. y = 8 x-5…

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Q: A) Find the Laplace transform of (2 03

A: We have to solve given Questions.