Find a unit vector in the direction in which f(x, y, z) + == Z y² increases most rapidly at P(1, 2, −2), and find the rate of change o at P in that direction. NOTE: Enter the exact answers.

Q: If f(x) f'(x)= -3x sin²(x) + 3x cos² (x) + 3 cos(x) sin(x) = 3x sin x cos x, find Find f'(4) =

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Q: Let f be a continuous and twice differentiable function. Let f'(3)=0 and f" (3)=2. Select all that…

A: givenf'(3)=0

Q: Evaluate the following integrals: 8 3 S(4 + 3√x) (2x + √x ³) "dx

A: SOLUTION-

Q: Which of the function is not an exact equation of the first order?

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Q: Evaluate the following integral. z+7 z(z²+9) dz

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Q: Tutorial Exercise Determine the set of points at which the function is continuous. G(x, y) = In(x² +…

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Q: sinx What is the integrating factor of (1+x) y + 2y = - 1+x

A: We have to find integrating factor for given differential equation.

Q: What is a suitable integrating factor that can be used to solve the equation dy cos(2x) = 0 O A. OB.…

A: To determine the suitable integrating factor that can be used to solve the equation.xdydx+2y-4xy-e-x…

Q: 15. Find the limit. lim X48 lim X-8 sin 15x 19x sin 15x 19x =

A: See this solution in below.

Q: 1. y' + ytanx = COSX; y(x) = (x + c)cosx; y(π) = 0

A: y'+ytanx=cosxy(π)=0proove that  solution isy(x)=(x+c)cosx

Q: Find the present value of $6000 payable at the end of 3 years, if money may be invested at 8% with…

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Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and…

A: Given data:- The given angle is, θ=80° The given diameter is, d=12 in So, the radius is, r=6 in.

Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy4 + 2y)dx + (2y³ + 2x²y +…

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D.4 O E. None of the Choices alt + dx…

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Q: the space curve (t) = (2t, t², 2t)

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Q: (a) J x² dx 3x + 2 x + 7 (b) 6) [ √2+1 da dx

A: Since multiple questions are asked, I am answering first question

Q: (d) Let y(x) = [tan-¹ (√)]4. Find y'.

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Q: Draw the unit circle and then shade in an arc of the circle's boundary with a shaded arc length of…

A: Length of arc, l = r * theta  Where, r = Radius of circle       theta = Angle subtended by arc at…

Q: Find a general formula for f(n). ƒ(x) = (x + 7)−¹

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Q: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

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Q: Evaluate the difference quotient for f(x) = −x³ +· O 3x²+3xh-h² O h² O-h² O-3x²-3xh-h²

A: See the details solution in below

Q: Evaluate the following limit: lim x ¹sin(8x). x → 0+ O O lim x-¹ sin(8x) = -8 vant lim x ¹sin(8x) =…

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A: To find the value of C

Q: Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0 and the plane 3x +2y + z = 6.

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Q: Question 9 Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y +…

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Q: Which of the following is TRUE about the differential equation x- dx O A. The equation is…

A: We have to find form of given differential equation.

Q: compute the acute angle formed by the asymptotes of the hyperbola x^2-3y^2-8x=14

A: Explanation of the answer is as follows

Q: Which of the following equations can be made into a linear differential equation? OA. (x² + xy)dy -…

A: Option D

Q: Which of the function is not an exact equation of the first order? OA (e³ + ycosx)dx + (xe³ + sinx +…

A: If a first order Mdx+Ndy=0  is exact then  ∂M∂y=∂N∂x.

Q: f(x)=(2x+1)^4. A) Find an equation for the tangent line to the graph of ff at x=2…

A: Givenf(x)=(2x+1)4

Q: Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 OA. O B. OC. ev eLny HA O D.y…

A: given    y(x+y+1)dx+x(x+3y+2)dy=0   it is of the form Mdx+Ndy=0   where M=y(x+y+1),    and…

Q: Evaluate the following integral using trigonometric substitution. S dx (x²-36) 3/2 " X>6

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Q: Find all values of n such that y = x" satisfies x²y" - 20y = 0

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Q: Similarly, approaching along the y-axis yields a limit equal to 0. Since these two limits are the…

A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: We have to find the value of c.

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

A: Given query is to find the distance between A and B.

Q: Find f'(x) and simplify. f(x) = 8x*(x³ -9) 3 Which of the following shows the correct application of…

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Q: Evaluate the following integral. 9 4 dx 1-√√x

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Q: Find the total area bounded by the graphs of f(x) = 3x³x² - 10x and g(x) = -x²+2x. O 32 units² O 8…

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Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x₁

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Q: (Question-Solution-Final Answer-Conclusion format) E. Generate solution of the first-order…

A: The solution of given exact differential equation is as follow.

Q: 23. The accompanying figure shows the graph of y = -x² shifted to two new positions. Write equations…

A: Given: The figure shows the graph of y=-x2 shifted to two new positions. To write the equations of…

Q: Which of the following is a non-homogeneous function? O tan³y/x xLnx − xlny x³ − xy + y² 3 2 - (y² +…

A: function f(x, y), if it can be written  by writing x = kx, and y = ky to form a new function f(kx,…

Q: Which of the following equations has a solution of the form F(x,y)= A. 2x + 3y + (2y + 3x) dx = 0 dy…

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Q: Which of the following equations can be made into a linear differential equation? A. (x² + xy)dy -…

A: To check: Which of the given differential equations is linear?

Q: Exercises  tell how many units and in what directions the graphsof the given equations are to be…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: (6) ft sin 2t dt.

A: We need to find out the integration.

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: the ideas presented in this section, what do you think is thearea under the curve of y = 2- x…

A: Given:curve is y=2-x we have to find the area under the curve bounded by x-axis and x=-4.we will use…