#3: Solve the initial value problem "+2y-63y0, y(0) = y(0) 1, y'(0) = -1

Q: 1an with a₁ = 2, an+1 = an with a₁ = 3, an+1= 1+sin(n) n 3n-1 2n+5 an an v. vi. n=1

A: (v) Given that the series is                  Thus, the series is convergent by the ratio test.

Q: dy Use implicit differentiation to find without first solving for y. dx x² + y³ = 1

A:

Q: dy Calculate using implicit differentiation. dy dx dx 27x=y4

A:

Q: Use the Product Rule to find f'(1) given that f(x)=x³ex

A: f(x)=x3ex

Q: and Y. If Zxy = -5y, what Assume z is a smooth function of x can you say about each of the…

A: Answers: (a) −5y(b) 0(c) −5Explanation:Step 1:

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

A: Solution of the above mentioned problem is provided below for further queries u may ask in comments…

Q: Find an equation of the tangent line at x = a. 2 y=x-xia=2

A: y=x−x2;a=2Using the power ruleddxxn=nxn−1

Q: a. · b = . ) Find a ⋅ b if |a| = 2, |b| = 2, and the angle between a and b is - radians.

A: a • b = 3.75877  Explanation:

Q: | Suppose f (x, y) = 2x² + 1xy − 2y², P = (2, −1), and u = A. Compute the gradient of f. 15 ( 17,…

A: Therefore, the required answers are a) The gradient is (4x+y)i+(x-4y)jb) gradient at the point…

Q: let F(x)=f(x^7) and G(x)=(f(x))^7  You also know that a^6=12 , f(a)=3,  f prime of a = 11, f prime…

A: The objective of this question is to find the derivatives of the functions F(x) and G(x) at the…

Q: Find f'(x) if f(x)=7e6x f'(x)= 0

A:

Q: Differential equations have been used extensively in the study of drug dissolution for patients…

A: Answer is given below:  Explanation:Question 1:Answer:

Q: 11+2i/4+3i

A: The expression in a + bi form is: 2−iExplanation:The given expression is: 4+3i11+2i​ First, multiply…

Q: Please review and solve problem 1 part 'a' and 'b' and explain how the answer was found. Problem…

A: All solutions to the given question are explained in the explanation section.Explanation:Solution 1…

Q: e exact area of the surface obtained by rotating the curve about the x-axis. 1 1 y = + ≤ X ≤ 1 6 2x…

A:

Q: (a) Let v(t) be a differentiable vector valued function of t. If v. (dv/dt) = 0 for all t, can we…

A: The objective of the question is to determine if we can say anything about the magnitude of a vector…

Q: Consider the parallelogram with vertices A(-3, 0), B(-1, 3), C(5, 2), and D(3, -1) Find AB and AD,…

A:

Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: Find a rational function that may have the given graphs.

A: R(x) = {-4(x+3)(x -2)^2}/{(x- 4)(x+2)^2}Explanation:Step 1 -The numerator of a rational function…

Q: y = (lnx + C)/x is a solution to the differential equation (x^2)y' + xy = 1 a) Find a solution a…

A: please see the attached solution belowExplanation:Hope it will helps youplease ask if you gets any…

Q: Find the third derivative of f(x) = ebx (ebx + e³-bx), where b is a parameter, and calculate its…

A: The third derivative of f(x) = ebx(ebx + e3 - bx) is f'''(x) = 8b3e2bx and f'''(0) = 8b3.…

Q: Find the exact length of the curve. y = 1-ex 0 ≤ x ≤ 5 -V1+e -10 - n -10 +1 ++ (1) √2+1 √1+e -…

A: The length of the curve of function f(x) over the interval  is The given curve equation is  ,

Q: F(r,s,t) = r(6s+2t²),

A: F(r,s,t)=r(6s4+2t2)Using the power ruleddxxn=nxn−1

Q: A real estate office manages an apartment complex with 40 units. When the rent is $1594 per month,…

A: A real estate office manages an apartment complex with 40 units. When the rent is $1594 per…

Q: Verify that there exists a function g: R² → R² such that u = (u,v) = g(x) for the system S4xu² +…

A: The determinant of the Jacobian matrix of F at the point (1,1,−1,−1) is 15, which is nonzero.…

Q: Calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables…

A: Please find the attached file for details....Thank you....Explanation:

Q: Suppose you sell skateboards and equipment. Grip tape costs you $2 for each foot, Each set of wheels…

A: Let G, W, B, T, and D represent the amount of grip tape, wheels, bearings, trucks, and decks…

Q: Are these lines parallel, -2_2-1 -2 2-1 and -1+3 Explain. -2 10

A: Yes, the given lines are parallel.Explanation:Step 1: Given,…

Q: dy Use implicit differentiation to find without first solving for y. dx x2 4 dy da + = 25 y² = 1

A:

Q: lim (√√x22x - x) 81x

A: −1Explanation:If you have any questions please let me know in comment box thankyou.

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS.

A: Answer : option (b) 2eExplanation: (7) Given,  f(x)=exx​ We know that,…

Q: 5. Use the definition of the derivative to find the slope of the tangent line to the curve y = 2x² -…

A: According to the definition of derivative we can write as follows Given Function

Q: Let y = tan (3x+5). Find the differential dy when x = 1 and dx == 0.2 Find the differential dy when…

A: The answers have been provided.Explanation:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: (-5, 2, 1) Explanation: Here, given equations of lines are…

Q: Compound Interest Match each formula for A with the correct name. Match each variable with its…

A: A = P(1+rt) - This formula represents simple interest formula, where:A is the total amount after…

Q: Let f : R → R be a function defined as f(x) = ⌊x⌋, where ⌊x⌋ denotes the greatest integer less than…

A: Greatest Integer function: The greatest integer function is a function that results in the integer…

Q: (a) Find the extreme values of f(x) = 2x3 + 3x2 - 12x + 1 on the interval (0, 2). (b) If f' (x) =…

A:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Two planes intersect each other as the cross product of normal vectors is non-zero.Explanation:…

Q: Find the arc length of the graph of the function over the indicated interval. y = = 3231(x² + 1) ³/2…

A: Arc length = 21 unitsExplanation: Given function, y=32​(x2+1)23​ Then, dxdy​=(32​(x2+1)23​)dxd​…

Q: Compute the exact value of the differential dy if y = 2ln(1+√√x) - if x = 4 and dx = 0.5 4 +12 3x…

A: Therefore, the required answer is dy=1/8Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Consider the following time series data Month 1 2 3 4 5 6 7 8…

A: The answers are given below please have a look.Explanation:

Q: = Water is flooding into a basement at a rate of f(t) = -2√√t + 5. Water is being pumped out at a…

A: a) 6.2288 ft3        b) -0.989 ft3/hr         c)  Volume max. @ t=1.457 hrs,    Total amount of…

Q: The accompanying figure shows the dimensions of a light bulb at 10 equally spaced points. 1.60 3.20…

A:

Q: Find volume by revolving the region bounded by y=sin(x) and y=0 between x=0 , x=pi about the y axis…

A: To find volume by revolving the region bounded by between  about the y-axis by using shell method.

Q: 8. The magnitude of vector [a,b,c] is¸ 9. The magnitudes of vector [a,b,c] and vector [-a, - b,-c]…

A: Magnitude of a vector is given by  is given by

Q: Evaluate S 6x In (5x)dx. 1/5 S 6x In (5x)dx= 1/5 (Type an exact answer.

A: The given integral

Q: Find the derivative of the function. x+2x-2 y= x-2x+2 OA. y=. OB. y'. O c. y=. 4x-8x (x²-2x+2)² OD.…

A:

Q: Use the graph of the function f shown to estimate the indicated limits and the function value.…

A:

Q: Solve the following system of equations using any appropriate method of your choosing: • x-y+z=8…

A: The correct answer is:(x,y,z)=(3+2z,-5+3z,z)Explanation:

Q: PLS HELP ON ALL ASKED QUESTIONS PLS

A: Solution is attachedExplanation:Step 1: Step 2: Step 3: Step 4: