Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3) Vw(17, 6, -3) = tan (3), 17 + 17 tan (3), 17 + 17 tan (3)

Q: Answer the following True or False. If f(x)dx 0 and f(x) is continuous, then a = b. O True O False

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Q: Derivatives of trigonometric functions Find the derivative. 1. y = 3sin x +3 cos x - tan x

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Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

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Q: (ii) sec2 (x) dx

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Q: 2. y = loga(x³ + 2x – 2)

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Q: Question 8 Use a difference identity to prove than tan(0 + 1) = tan(). PENCIL THIN BLACK V

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y²,…

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

Q: Find the gradient of the function at the given point. w = x tan(y + z), (5,13, -10) 2 tan(3)i,5…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: dx Example: Evaluate 3 + sin x + cos x

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A: Given information:  The x-sectional area of liver is given at interval of 1.5 cm. Note : The figure…

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A: Angle between planes and line of intersection of planes

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Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

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Q: Determine whether the lines are parallel or identical. X - 5- y+ 4 z + 8 5 4 x + 7 = y - 5 z + 23…

A: The directional vector of L1:v1=4, -3, 5The directional vector of L2:v2:-8, 6, -10   : -2 4, -3, 5v2…

Q: S x³et*dx

A: A detailed solution is given below

Q: True/False: The saddle point of the of the function f(x,y) = x² – e occurs at (0,0). - O True O…

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Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

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Q: dy Find for the following expressions: dx a) y = x5 In(3x)

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

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Q: ind the angle 0 between the vectors in radians and in degrees. (Round your answer for part (a) to…

A: Given problem:- u= 7i+j v=-6i+8j To find:- Angle between vectors in radian and degree

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Q: For what value(s) of z on [0, 7] is the value of f(z) = sin z +1a maximum?

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Q: At a point 160/3 feet from a building, and in a horizontal line with its base, the angle of…

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Q: From a window 30 feet above the street, the angle of depression of the curb on the near side of the…

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Q: Find dy and simplify whenever possible. dx 1. y = arcsin + 4-x2 2. y = In(e¯* + xe¯*) sin x cos x…

A: To find derivative of given function.

Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: 4. The graph below depicts a function g(r). Its one asymptote is indicated in red: 4 -5 -4 -3 -2 -1…

A: Find your answer below

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Q: b. S sech x = 2 Arctan(e*) + c

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Q: Where is the function decreasing? * (-1,3) (-2,1) (0,1) O (*-1) O (*, *) O (-1, ) O (-*, 3)

A: A function is said to be decreasing in an interval in which on increasing the value of x, the value…

Q: Г(81)

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

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A: To find volume of parallelepiped.

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A: Let the edge length of the cube be 'a' units

Q: 4-x² 4. Evaluate [*, [* (r² + y°) dz dy dx. 4-. Hint: This iterated integral is a triple integral…

A: Cylindrical Coordinates:       Put x= r cosθ and y=r sinθ and z=zthen,      r = x2+y2 and θ =…

Q: Use loganithmic differentiation to evaluate f'(x). 10 (x+2)" f(x) = (4x- 16)" %3D 11

A: Given problem:- f(x) = (x+2)10/(4x-16)11 To find:- Use logarithmic differentiation to evaluate…

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Q: Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each…

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Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 5. x = c1coswt + c2 sinwt

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Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations hat are…

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Q: Which of the following trigonometric expressions is NOT equivalent to 1? * csc? 0 – cot² 0 cos? 0 +…

A: To determine which of the given trigonometric expressions are not equal to one.

Q: Direction: ate the following arbitrary constants to obtain the DE. а 3. y = () + bx

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