Differential equation: Families of Curves * w/ complete solution and sketch. Obtain the differential equation of the family of plane curves described below and sketch several representative members of the family 1.) circles passing through the origin and (0,4)

Q: On the interval shown, for which graph is f' positive and f"' negative? OA. OB. Q O C. z Q 2 OD.

A: To choose the graph which describes the given characteristics

Q: Question 1 ( (a) ) ) For the function (b) ( transform 3 f(t) use the definition of the Laplace…

A: Given function is (a) f(t)=30≤t<2e2tt≥2and (b) L-13(s+5)(s-2)

Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

A:

Q: Compute the flux of the vector field F = xỉ + y) + zk through the surface S, which is a closed…

A:

Q: Question 8 Consider the indefinite integral U= du = x5 (x6 + 4)6 This can be transformed into a…

A:

Q: 1) Let an = 3+2(n-1). Write the first 5 terms of an. Find Σ10% ακ k=1

A:

Q: The answer

A: We are asked to find the increase in cost if the production level is raised from 1200 units to 1800…

Q: Given f(x) = 19x - 3| +2 25. f'(²-) = If f(x)=(√3x-2)5 then f'(9) = Given f(x) = sin(3x)² 26. f'() =

A:

Q: Question Find the Laplace transformation s²+2 S3 L {f(t)} if f(t)= (t + 1)² ? O None of them…

A:

Q: Differentiate. y' = y = 3 sec(x) - csc(x)

A:

Q: 11 Rewrite sin (x+ 11) in terms of sin a and cos x. Simplify your answer. Enclose arguments of…

A:

Q: Find the most efficient substitution for the integral textbook. Enter f(2). Answer: e²x dx 1+Ax /₁…

A: we know   ∫11+x2dx=tan-1(x)+cdexdx=exI=∫e2x1+e4xdx

Q: 2. Test the following series for convergence or divergence. If converge find its sum. Indicate the…

A:

Q: 5. Consider the polynomial graphed to the side. Answer the following questions using that function.…

A: We need to interpret the graph.

Q: Vector v is shown in the graph. पं احبه N T > 51 a 3 0 -1 N do O ||v|| = 9.220; e = 54.462° 2 Which…

A: To determine the magnitude and direction of given vector.

Q: Determine all values of x. (if any), at which the graph of the function has a horizontal tangent.…

A:

Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of…

A: To find the rate at which the area is changing

Q: en the graph below, solve the following inequality: g(r) > 0 +10 + 80 9 8 7 -8-7-6-5-4-3 54 6543 2…

A: Given query is to solve the inequality.

Q: Find the derivative of the function. y = sin ¹(cos-¹(t))

A:

Q: mpute the following integrals using suitable method. [xy dxdy, where R is theregion bounded by y=1,…

A:

Q: -X 17) y=e^· cos(2x); dy = ? -X A) -ex (cos 2x + 2sın 2x) B) e (sin 2x- ccs 2x) c) 2ex Sin (2x) -X…

A: Given:- y=e-xcos2x

Q: sin³ x + cos²x sinx = 2

A:

Q: A tank is full of water. Find the work W required to pump the water out of the spout. Use the fact…

A:

Q: 7s +5 s² + 25 Is true or false? Select one: O True O False Give your reasons } = 7 cos (5t) + sin…

A:

Q: (3) ( ) (A) Find the volume of the solid under the paraboloid z = 2x² + y² and above the rectangle…

A:

Q: 3. Solve the following inequality: x³ + 2x²-3x x-4 ≤0

A:

Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: › = √²) f(u)du what is dg / dx? Suggestion: Let x² = v and use the chain rule. _g(x) =

A: Given query is to find the derivative.

Q: hether the matrix is invertib

A: We have to consider the given matrix is invertible or not

Q: If f(x)= f'(x) = = tan z sec x -4

A:

Q: Show that the eigenvalues of A-¹ are ¹. 27 Show that A"x = λ"x if Ax = λx.

A: Given λ is an eigenvalue of A. So there exists a nonzero vector x such that Ax=λx....(i) 1.Since A…

Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

A:

Q: Solve the following initial valuc problem using the method of Laplace transforms y" - 4y + 5y = 8c³;…

A:

Q: Use logarithmic differentiation to find dy/dx. y = x²/x X>0 dx ||

A:

Q: Quality management charges 7.5% of the monthly rent on properties it manages. If they manage nine…

A: Given Quality management charges (r)=7.5% of the monthly rent on properties it manages total number…

Q: Use the Second Derivative Test to find all local extrema, if the test applies. Otherwise, use the…

A:

Q: Evaluate the integral by making the appropriate substitution: u = f2¹ (25 - 4) 43³dz = dx 43 fz¹ª…

A: To evaluate the integral.

Q: 4. Find an equation of the tangent plane to the surface z = xy+8 xy-2x at the point (1,1,–10)

A:

Q: Differentiate the function. F(t) = (3t - 5)² F'(t) =

A: Let's differentiate given function.

Q: -2 Determine if the columns of the matrix A = 4 O No Yes 1 4 0-4 -4-6-8 are linearly independent.

A: The given matrix A=-21440-4-4-6-8. We have to check the columns of A are linearly independent or…

Q: The volume of a sphere is increasing at a constant rate of 1827 cubic centimeters per second. At the…

A: To find the rate of change of surface area of sphere.

Q: Find dy/dx by implicit differentiation. 7x²y + 4y²x = -1 dy/dx =

A: Given query is to find derivative.

Q: Differentiate the function. F(t) = tº + e⁹ F'(t) =

A: Here is the solution:

Q: uestion 1: For the graph of the circle below whose equation is of the form (x-h)²+(y-k)² = r2, enter…

A:

Q: Find a "cartesian" equation for the circle which is given by the polar equation r = 2 sin 0, and…

A: Given query is to find the Cartesian equation and the centre of the circle.

Q: The volume of a sphere is increasing at a constant rate of 198 cubic feet per second. At the instant…

A: let Volume = V V = 43πr3S = 4πr2dVdt= 198 ft3secfor an intance V = 18 ft3

Q: er the equation of the parabola graphed below, using the vertex form y = a (x-h)²+k. y = (-1,0)…

A: To solve the following problem using graph

Q: 14. √9-x² x2 S dx

A:

Q: Question Which of the following is the Laplace transformation O L {f(t)} if f(t) = (cos(-3t))² ? s²…

A: