3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector i+j+k. b. The line through P(1,2,-1) and Q(-1,0,1).

Q: A 20-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1…

A: This question can be solved using the concept of differential equation.

Q: We know that F is an antiderivative of f, so to: O a) lim (F (b) - F(a)) a 0 Ob) lim (F (b)-F (a))…

A: Here given that, F is an antidervative of f, so we have to find the value of ∫0bf(x)dx=?

Q: Find the volume and the dimensions of the largest rectangular box in the first octant with three f…

A:

Q: 16 You know that f(x) = g(x) + 6 and that * S™ ƒ f(t) dt = 27. You also know that f(4) = 4 and f(16)…

A:

Q: Problems: Solve the following differential equations: 3- (2x+y)dx+(x-2y)dy=0

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Please do not handwritten your answer, pure typewritten only!

A: We have to prove that product xy of two real numbers x and y is nonnegative if and only if the…

Q: 3x + 5, 13+¹6, Find a value of x, if any, at which f(x) = If f(x) is continuous for all values of x,…

A: Given: Notice that 3x+5 is continuous for x<4 and 13+16/x is continuous for x>4. Now, we need…

Q: Let S = { 1 − (−¹)ª | n € N}. Determine inf S and sup S. Justify. (-1)" n

A: Let us define set S  by giving values to n so that     S={2,0,2/3,0,2/5,...}. Hence S={1+(1/n) if n…

Q: Find the exact length of the curve. y 1x²-1-In(x), = 4 2 1 ≤ x ≤ 8

A:

Q: Find the equation for the tangent line of the graph of 4 y = x² at (-2, 16). Equation:

A: Here we have to find the equation of the tangent line of the graph y=x4 at (-2, 16)

Q: A company can produce a maximum of 25 widgets in a day. If they sell x widgets during the day then…

A: Above question is solved.

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

A:

Q: 2-x x+²√√x+2-√√3x-2 c) lim-

A:

Q: d dx [47 tot 1 3x17 5 13 + 10 L 25 +100

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: 4) Find equations for the planes: a. The plane through P, (0, 2,-1) normal to n=3i-2j-k

A:

Q: State

A:

Q: 3) Find equations for the lines: The line through the point D/2 g. The line through (0,-7,0)…

A: Equation of line in 3D

Q: Solve the given initial-value problem. dx y - x = 6y², x(8) = 1 dy x(y) = Give the largest interval…

A: Given problem:- Solve the given initial-value problem.   ydx/dy-x= 6y², x(8) = 1

Q: ate the following integral using polar coordinates 17 'yx² (x² + y²j2dxdy

A: Above question is solved.

Q: Find the cumulative density function for the given probability density functio k(x) = 1.4 e 1.4x,…

A:

Q: If G is an antiderivative of the function g, so the following integral is equal to what option? 1-26…

A: Given problem:-

Q: an integral corresponding to the area of the region bounded by the curves of the functions f and g…

A: f(x) =x2 -4x  g(x) = -x2 here area function = f(x) - g(x) = x2 -4x  -(-x2 ) = 2x2 - 4x

Q: al fraction decomposition of the rational proper fra P(x) A B + x+1 x-3 at's the value for A and B?…

A: We have to choose the correct option from the given options according to the given information

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: To find the absolute extema first I have find the derivative of f(x) , set them equal to zero and…

Q: 12. A plane 77₂ intersects 7₁: 4x-2y+7z-3-0 at right angles. Two points lie on 77₂: A (3,2,0) and B…

A: Given equation of planes π1 ; 4x-2y+7z-3=0points  A( 3, 2, 0 )  and  B ( 2 , -2 , 1)  lies on  the…

Q: derivative. (a) lim (b) lim Ax→0 In(e¹ + Ax) - 4 Ax In w w 1 w 1 =

A: Using L hospital rule

Q: A thermometer is taken from an inside room to the outside, where the air temperature is 20° F. After…

A:

Q: a. The line through the point P(3,-4,-1) parallel to the vector i+j+k. b. The line through P(1,2,-1)…

A: a) Here, the given vector is: v=i+j+k=<1,1,1> And, to find the line equation which passes…

Q: Consider the function f(x) = (3x² − 4)(x² + 6). (a) Compute the derivative of f(x) by multiplying…

A:

Q: Problems: Solve the following differential equations: 9- (e + In y)dx + (+)dy=0 y

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 1. (2xy² + 2y) dx + (2x²y + 2x) dy = 0, 2. + 6x) dx + (In x - 2) dy = 0, x y(1) = 3 y(e) = 1

A:

Q: d dx [3 sin³ (tan √x² + 3x²)] d [(x² + 1) cotx dx 3 cos x csc x

A: Given

Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: Which of the following gives the volume of the solid obtained by rotating the region R about the…

A: We know that the area of the curve y=f(x) , the X axis and the lines x=a ,x=b is revolving about the…

Q: 9. a. Explain why the Cartesian equation 2r-5y +3= = 2 does not describe the plane with normal…

A:

Q: 8. Determine the area bounded by x = -y² + 4y and the y-axis.

A:

Q: (3 - x) dx is equal to ° S (3 − x) dx + ["' (3 + x) dx °₁ (3 - x) dx ° L₁ (3+2)dz + f (3-2) x) dx x)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Solve the differential equation (24xy + 40y²) + (8x² + 40xy)y' = using the integrating factor µ(x,…

A:

Q: Verify that the indicated function y = (x) is an explicit solution of the given first-order…

A:

Q: Matrices A and B below are row equivalent. For each of the concepts following, choose (check) one…

A: See the answer below

Q: dy Give the coordinates of the point where dt y = sin(t)- t³ O (0,0) O (0.535,0) O (-0.535,0) O (0,…

A:

Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

A:

Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges.…

A:

Q: 7- cos y dx + (x siny-cosy)dy = 0 8- (1+ y²)dx + (2xy + y² + 1)dy=0

A:

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: Graph the following function. Show at least two cycles. Use the graph to determine the domain and…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Find an explicit solution of the given initial-value problem. dy_y²_ 1 = y(4) = 4 dx 1 ||

A: The objective of the question is determine solve the differential equation.

Q: Let r(x) = f(g(h(x))), where h(1) = 5, g(5) = 2, h'(1) = 9, g'(5) = -2, and f'(2) = 5. Find r'(1).

A:

Q: = [ (23a)" e1¹0z da, Consider the integral n is a natural number greater than 1, When applying…

A: Given problem:- J = ∫ (23x)n e10x dx