2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the direction of A = 2i+j-2k

Q: Evaluate the following integral using inversion of order: So ²5 dydr Remember to show complete…

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Q: Use linear approximation, the tangent line, to approximate √49.1 as follows: let f(x)=√x the…

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Q: 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5)…

A: First we need to find the vector and then find the opposite components of it.

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Q: Lim x tends to pi/4- (LHL) √(1-√sin2x)/(pi - 4x)

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A: Let's solve limit problem.

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A: We have given a function f=|x| , we have to find g(x) with the help of graph

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: nd the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -x³-7x…

A: Use derivative for finding the increasing and decreasing interval.

Q: Let a be a real number. Evaluate the following integral: So fx + y dxdy

A: We have to evaluate the integral ∫0a∫y-1y+1 x+y dx dy  where a is a real number.

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A: Given:

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A: We have to find solution of differential equation.

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Q: For a given cylindrical tank, the radius is 7 m and the height is 15 m. The tank is filled to a…

A: Use workdone formula for finding the work

Q: Test the series below for convergence using the Ratio Test. n+ 3 3n+3 The limit of the ratio test…

A: you have entered value of an instead of f(n) .

Q: Find the distance from the point (3,-7,-1) to the plane -x + 5y + 2z = 34.

A: Here is the solution:

Q: 3. I Graph of f Graph of g The graphs of the functions f and g are shown in the figures above. Which…

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Q: The alternating series En-1 (-1)" is diverge. n³ 2n³+3 True O False

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Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.

Q: The equations of three lines are given below. Line 1: 6x+4y=-8 Line 2: y = x-3 Line 3: 3y = 2x+4 For…

A: The given lines are:Line 1: 6x+4y=-8Line 2: y=23x-3Line 3: 3y=2x+4

Q: L sin2t cos3t

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Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - z = 1…

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Q: Choose the angle (in radian) between the following two vectors u = and U = O 2.059 00 O None of…

A: We know that angle between two vectors a and b cos(θ)=a.b|a||b|

Q: Given the points A(-8, 2, 3) and B(-8, 2, -4). Question 3 b) Find the intersection of the line…

A: Question 3.The given points A-8,2,3 and B-8,2,-4.

Q: 6. If : G H and 8: H K are both homomorphism, so is 0. • : G → K.

A: We can solve as follows

Q: Let à = i-5j - 2k. Find |āl.

A: Using the formula if  a→= x i^ +yj^ +zk^then a→=x2+y2+z2

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Q: Find an explicit solution of the given initial-value problem. 1 y(4) = 4 y = dy dx = y² x² - - 1

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A: Use derivative and length of curve formula for polar curve.

Q: S In (x) √xln(x)-x =dx

A: Please see the below picture for detailed solution.

Q: Using implicit differentiation, find dy dx √xy = − 1 + xy

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Q: Drag and drop your answer into the box: (a) An antidervative of f(x) is (b) The indefinite integral…

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

Q: (1) (x²+2x) dx = (3 - In x²) dy separable exact linear in x linear in y homogeneous Bernoulli in x…

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Sketch the following surface: (2+4)² + (y-1)² = 1 a.) Draw the projection on a xy plane Show…

A: The eqaution is given  (z+4)2 +(y-1)2 = 1

Q: Evaluate the integral. 7/4 O [(10sect)i-(3+ sin t)j - (2sec t tan t)k)]dt (2√√2-37-4 2 10i + O 10i +…

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Q: Let f:R-R,g: RR and h: R→→R be differentiable function such that f(x)=x²+3x²+4 g(x)=x and…

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Q: Evaluate the integral. 7/4 O O [(10sect)i-(3+ sin t)j - (2sec t tan t)k)]dt (2√√2-37-4 2 10i+ 10i +…

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Q: f(x) = 2 cos x - cos 2x.

A: Given function f(x) =2 cos x - cos 2 x    ; [0, 2π]

Q: Find the root's 51 of Complex equation:

A: Given:      5√(-1)

Q: Solve the given differential equation by separation of variables. exy dy =e-¯V + e-8x - y dx

A: In this question, we want to solve the given differetial equation using separation of Variables.

Q: Let a be a real number. Evaluate the following integral: So fx + y dady -1

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Q: The reverse order of 2 2 1 Jo Jy x 1 sinx cos dxdy is sinx cos dydx False True O

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Q: 27. Consider the function h(x) = 2x²e-x² a) In two or three steps, write the properly simplified…

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Q: \(\) The geometric representation of the equation -4x² - 4y² = -12 is not a cylinder in R². Select…

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Q: Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How…

A: This question is based on Compound interest formula.

Q: Graph the function. = (x) = -4 X for-4<x<-1 for -1 < x < 4 -x² +16 for x ≥ 4 16 11 V 15- 14. 13- 12…

A: Consider the function  Consider the function    z(x)=-4                     for  -4&lt;x&lt;-1x…

Q: Determine the point on the curve y = 19x closest to the point (0. line through (0, 5) and the…

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Q: For the sequence an = an-1 + an 2 and a₁ = = 1, its first term is 1 its second term is 1 its third…

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