Find the gradient of the function at the given point. g(x, y) = 6xeYlx, (14,0) Vg(14, 0) :

Q: Written Works Evaluate the following Integrals. 1. S sin ycosy dy 2. sin3x dx 3 1 3. Jс S cos-y dy |…

A: Given: 1). I=∫sin3ycosydy  ....(1)   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; n≠-1…

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Q: 2. Locate the centroid (x, y)of the following areas: a) y3D Vx/2 + 2r/3 %3D I 2 ft

A: Given:    Centroid of the colored figure x,yWhere,x =MyM      &       y =MxMMy = ∫02xfx-yxdx…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 4, 3) 12x…

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Q: Question Evaluate the following limit using L'Hospital's rule. 10 lim 5* ( 3x2 24x +45 3x - 15…

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A: Explanation of the answer is as follows

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Q: a. Find all the asymptotes of the following functions 4x* + 4x3 + 12x² + 6x – 24 6x* + 8x – 9 f(x) =…

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Q: (a) Use Newton's method to determine 2 correct to 6 decimal places starting with an initial guess r1…

A: Let's find.

Q: (-2 if XS-1 S(x) = {x² -3x+8 if if -1<x<2 x22

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Q: Let f(x) = Va and g(x) = x² – 1. Find go f and determine its domain. |3D %3D

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Q: Let f(x) = VT +k, where k is a constant. Suppose we want to evaluate | f(x) dx. f(x) dæ dx – 2 dx +…

A: Given:   Let fx=π-2x+k then      ∫fxdx=∫π-2x+k dx                      =∫πdx-∫2xdx+∫k dx taking…

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Q: Solve the differential equation dy ; y(0) = –1. %3D da Vx³ +1 There is no need to isolate y.

A: We know, ∫xndx=xn+1n+1+C , C is a constant and n is any real number.

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Q: is a p-series. ... 27 37 47 57 Select one: O True O False -17

A: The detailed solution is given below Thank you

Q: 144-inch length of pipe is to be cut into 3 pieces. The second ece is twice as long as the first…

A: Topic:- geometry

Q: what is of the waximal domain gla) = Inf2x)

A: Maximal domain is the largest set of real numbers for which the function is defined. The given…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = el2"i +e-j 12ts K(t)

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Q: In general, if f(x) is real and continuous in the interval from x to xy and f(x1) and f(xu). between…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

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Q: Let f(x) = x In(1+x*). For all x E [-1, 1], it is known that (-1)" In(1+x) = -xn+1 %3D n+1 n=0 1.…

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Q: Find the area of the region enclosed by the rose r = 10 cos 30. NOTE: Enter the ezact answer. A =

A: Here, the polar curve is r=10 cos 3θ which is as shown:

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Q: In the differential equation (1 + 3x sin y)dx - x2 cos ydy = 0 , we let the substitution w =…

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Q: _13. What is § 2sinx cos x dx? cosx A. In2 +C В. C. +C +C D. In2 _14. Which of the following has…

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Q: Determine the following functions as homegenous or not, if homenenous state the degree. 1. √x-y…

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Q: dy 2 Solve (x2 - 1)+ 2xy x2-1

A: (x2-1)dydx+2xy = 2x2-1dydx+2xx2-1y=2(x2-1)2this Diff eq is Linear Diff Eq.dydx+P(x) y =…

Q: Consider the following. u = i +j+k v = 21 + j - k Find u x v. Determine if u x v is orthogonal to…

A: u=i+j+kv=2i+j-ku×v=ijk11121-1u×v=i(-1-1)-j(-1-2)+k(1-2)u×v=-i-3j-ku×v=-i-3j-k

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Q: Find the general solution of the following linear second order homogeneous O.D.E.: ý + 2ý – 15y = 0

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Q: g. There is a removable discontinuity at = 1 and f(1) = 4 h. There is a jump discontinuity at z = 2…

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Q: 1. There is no function f(x) such thatS f(x) = f(x) + C. _2. If f(x) and g(x) are continuous…

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Q: Find the gradient of the function at the given point. g(x, y) = 13xeY/x, (5,0) Vg(5, 0) =

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Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, Р(5,…

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Q: A. Solve the following and show your solution. 1. Use the definition of Fibonacci numbers to find…

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Q: 5. Determine the intervals on which f(x) = -5x* + 40x³ – 5 is concave up or concave down using…

A: 5.The given function f(x)=-5x4+40x3-5 Note:    Multiple questions are given, we are answered with…