Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

Q: Determine the antiderivatives of the following functions: 1. V36-x² dx 2. 9x²+36dx

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Q: 4 2 6e"*+2dydx =? (a) 2 (e* – e?) (b) 2 (e10 – e°) (c) 2 (e16 – e?) (d) 2 (e2 – e?) (e) 2 (e64 – e?)

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Q: 2. (D² + 4)y = 5e* - 4x

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Q: 1) Use the definition of the derivative to find f'(x) f(x) = (4x + 1)(3 – 7x³) Step 1: Step 2: Step…

A: Topic:- function and it's Derivatives

Q: 2. For the parametric equation shown below, determine the value of (dyldx) and (d²y/dx?). x = 3t? –…

A: To find dydx& d2ydx2 using the given parametric equations.

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A: Solution is done in step 2

Q: 1. Consider A = (0,4, 2), B = (6,0,0) and C = (3,0,-1). %3D %3D (a) Find the unit vector in the same…

A: B-2A+C=<6,0,0>-2<0,4,2>+<3,0,-1>…

Q: L. Find the point/s of intersection of each of the following figures given below, draw the element…

A: Given: Now find the point of intersection between the curve y=x2+2 and the line x=2. y=x2+2 ;…

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A: Parametric equation of line passing through a point x0,y0,z0 in the direction of N=a,b,c is…

Q: Consider the solid obtained by rotating the region bounded by the given curves about the specified…

A: Since you have posted multiple questions as per guidelines we can solve only one question at a time…

Q: Mary, Martha and Lazarus lives in the same house. It takes Mary 2 h to clean the house alone. Martha…

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Q: d radius of the

A: If r = A cosθ + B sinθthen Centre is A2 , B2 and radius is A2 + B22

Q: 7. Each of the following statements is true. What can you conclude about the vectors i and i f: a)…

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Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

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Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: x = -2t x - 3 1 – y Given: line l1 : 4 = % – 8 and l2 2 y = 2+ 2t - % = 6 + 2t 1. If the given lines…

A: We have to find angle between the lines L1 & L2

Q: Q3. (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x2.

A: We have to find binomial expansion.

Q: 4. Determine the equation of the plane passing through the point (1,-4, 3) and parallel to the plane…

A: Explanation of the answer is as follows

Q: y =, x = 1, x = 4, and y = 0 is revolved about the y - axis.

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Q: Find the first three nonzero terms of the Maclaurin expansion of the function. (x) = e 6x What is…

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Q: 135 5. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: S. U. u.) 4

A: Let's find.

Q: Consider the piecewise function: 2x+8, x3 Determine the value of each limit. If the limit D.N.E.,…

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Q: Consider A = (0, 4, 2), B = (6,0, 0) and C = (3,0, –1). (a) Find the unit vector in the same…

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Q: 1 3 5 8 - 37 13) 3 8. 7 Ans. r = 3 0 - 37 0 37

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Q: Find the sum of the convergent series. 1.6

A: Gp

Q: Part 2. Use the integration techniques to solve for the anti-derivative of each fur I. S3p? tan p dp…

A: According to the company rule we can answer only the first question and rest can be reposted.

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Change the following polar equations to rec 6. 12. r = 4-cose

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Q: 1. The figure shows the graph of a function f (x) with domain 0 < x < 3. Which of the following…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Solve for the general solution using homogeneous

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Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: Find the length of the curve 7(t) = (2 cos(4t), 2 sin(4t), t) for –2 <t s8 Give your answer to two…

A: As we know that; The expression for the length of the vector-valued curve; L=∫abx't2+y't2+z't2dt And…

Q: 2. y=x² - 4x and y=-x² +2x. y² = x and x² –2x+3y= 2. 3.

A: Given÷

Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e*

A: The objective of the question is determine the differential equation.   Note -  As per our…

Q: 1- x² tx

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Q: The integral sin(x- 2) dx is transformed into f, g(t)dt by applying an appropriate change of…

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Q: 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the…

A: Volume of sphere   V=3π​r3/4 Percentage error in volume    ΔV​×100/V=3×Δr​×100/r =3*1*100/10*7= 4.3…

Q: a?z B. For each of the following functions z, find a2z and ду? a²z дх? дудх' дхду" 1. z = 2x2 – 5xy…

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Q: Use the Linear Approximation to estimate Af for f(x) = , when a = 2 and Ax = 5+x2 (Use decimal…

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Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

Q: d of Variation of Parameters: [D² - 8D + 16]y = e4%sec2 %3D

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Q: Convert to a rectangular coordinate. Convert to a polar coordinates. 5T 10. 11. (-4,4)

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Q: Exercise 4 * Suppose the following data points are generated by a smooth function f(x): 1/6 1/3 1/2…

A: We have to find best approximation using the composite Simpson's rule.

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: (sec2 x + csc2 x)cos2 x dx

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the line l1…

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Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: integration using substitution

Q: Consider the function g defined by g(x, y) = sin (T /Ty) + log3 (x – 3y) Do as indicated. 1.…

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Q: e2t (t3 + 5t – 2) - 6+ 5(s – 2)? – 2(s – 2)³ (s – 2)* 6 2 - | (s + 2)* (s – 2)? 8 – 2 Option 2…

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Q: Determine if the following function is periodic. If it is periodic find the fundamental period, p.…

A: period