Find zr if z = xyev, x = rcos(t), y = rsin(t), when r = 2 and t Zr TU 6

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A: Given: Interest = 5%

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A: Given acceleration of an object after time t is a→t=-2.i⏜+j^+3k^ Let the position vector of the…

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Q: 73. lim sin 3t t⇒0 2t

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

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Q: 4. For the second-order differential equation y" + 4y = -16 cos²x: a. Show that y = cos 2x + 2 is a…

A: We have to find a,b,c .

Q: Please show all workings in each question neatly and in detail. 1. Evaluate the following indefinite…

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A: The given function is fx=ex-2 which has a root in the interval 0,  2.

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Q: 8. y e²x dx = (4 + e²x) dy.

A: Need to find out the solution of the differential equation.

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Q: Use the tabular method and the properties of limit to find the limit lim ex-4 X-4

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Q: Evaluate lim 1-cos3x x→0 tan 2x

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Q: Differentiate the function. 1 2 =(√x + + + + + ) ² 3 v' = V

A: See this solution in below.

Q: Minimize the function M=3x² + 3y² subject to 2x+y=64 and find the values of x and y at which M is…

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Q: Use implicit differentiation to find dy/dx for the following: 2x^3 - y^3 - e^y = 10

A: This question can be solved using the concept of differentiation of implicit and explicit function

Q: Find all of the partial derivatives for each function: 1. f(x, y) = x¹ +6√-10 2. w=x²y-10y²z³ +43x −…

A: As per the guidelines I am supposed to do the first question among multiple questions. To get the…

Q: Question 1: Let f be a function and let h be a non-zero real number. Then the derivative (when it…

A: We have to tell true or false Answer (1)

Q: y = (0,1) mox: (1,12) 2.Write the equation of the given graph. U wwtaai-y 3. A pen consists of 4…

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Q: 12-14 Simplify the express 12. tan(sin ¹x) 13. sin(tan ¹x) 14. sin(2 arccos x)

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Q: The the following 14 (sec) S (Ft) 0.4 1.5 3.56.29.6 positions s of a car at time table 0.2.4 0.6 0.8…

A: Concept: The average velocity is average velocity=∆s∆t=s2-s1t2-t1Instantaneous velocity=st.....(at t…

Q: Find the polar form for zw, z/w and 1/2 where: z = 2(1 + i), w = 3(1+√√3i)

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Q: Consider the following graph of y = f(x): s What is the lim fx f(x) x-0 A.0 B. 1 OC. -1 D. 2 E. The…

A: From the graph we can see that as x tends to 0, f(x) tends to 1.

Q: Write cos(sin(x)) in an algebraic expression form.

A: the solution consists of substitution

Q: Evaluate the integral using integration by parts with the indicated choices of u and dv. (Use C for…

A: A detailed solution is given below.

Q: Find y' of tan(x²y4) = 3x + y²

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

Q: A cup of coffee is removed from a microwave. Its initial temperature is 199 degrees. After exactly…

A: In the given question: A cup of coffee is removed from the microwave, θ1=199∘C After 11 minutes…

Q: Solve the following differential equation: 4y'' +12y' + 9 = 0

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Q: x² - 10x (c) lim 9x²-x 2

A: L’Hospital’s Rule Formula L’hospital’s rule states that Note: The limit of the quotient of function…

Q: (d) s

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Q: Solve the integrals: (1) (c I₁ = 1 |x| x² + x| dx

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Q: A curve passes through the point (0, 2) and has the property that the slope of the curve at every…

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Q: If x= find dx y+2 2y/2y 4. B. B. Find y' if y = (2x2-3)(3x+2) 4x-1 48x³-2x²-8x+15 (4x-1)²…

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Q: Solve the following differential equation:    4y'' + 12y' + 9y = 0

A: we have to find the solution of given differential equation.

Q: Use PMT= $ 35800 P +) a home is $179,000. The bank requires a 20% down payment and three points at…

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Q: III. Eliminate the arbitrary constants of y = c₁ cos3x + c₂sin3x.

A: Given function, y=C1cos(3x)+C2sin(3x)

Q: Find the solution of the IVP: (1 + y cos x) dx - sin x dy = 0, y(1/2) = 1. Then, evaluate y(1.603).

A: This question can be solved using the concept of linear differential equation.

Q: x² - 10x x-0 9x²-x (d) lim

A: Given query is to find the limit of the expression.

Q: Given f(x, y, z) = x²y³z − 3xy²z³ + 5x²z − y³z, find fxyz

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Q: For y = f(x)=x²-7x³ +5, find dy and Ay, given x = 1 and Ax= -0.1. dy = (Type an integer or a…

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Q: )A. Let,g(t) be the solution of the initial value problem with g(1)-1 Find g(t) g(t) 1/(14) B. Let…

A: We have to find the solution of the given differential equation.

Q: Solve g) iv. using the lebiniz rule, differentiate the following functions with respect

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Q: Kindly exhibit that xzxx+yzxy=y2zyy if z=xy+yln(xy)

A: The given data is: z=xy+ylnxy To prove: xzxx+yzxy=y2zyy

Q: Find y' if y= 48x³+34x2-8x+15 (4x-1)² 48x³+34x²-8x+33 (4x-1)² If y = 3u² - 2u + 4 and u = x² + 3x -…

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Q: Find all values of where the graph of f(x) = 2x³-39x² + 240x-5 has a horizontal tangent line.…

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Q: Determine the solution of the 1st Ordered Differential Equa 3(x² + y²)dx + x(x² + 3y² + 6y)dy = when…

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