21) Differentiate implicitly x² = x²y+2y²

Q: Evaluate I se sech¹0d0. 4

A: We have to find out integral

Q: If the vector equation of a line is 7=(3, -5)+t(-2, 3), t€ R. the parametric equations are Ox=3-2t,…

A: Topic:- application of geometry

Q: What is the slope of the the tangent line to y=1/x^5+−1/x^3 at x=1?

A: Given y=1x5+-1x3 and x=1

Q: it a rock is dropped from a height of 288 ft, its poistion t seconds after it is dropped until it…

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Q: 52. y' - y = y³

A: We need to solve D.E.

Q: Solve the differential equation (2x + y) dx (4x + 2y − 1) dy = 0 O a. 5x 10y + In 10x 5y 2|= C O b.…

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Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: x = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your…

A: Topic:- application of derivatives

Q: If fa rsin xd a. -6 b 6312 C. 6 d - 3 2 = -x³ cos x + 3x² sin x + k fx x sin xdx, find k

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Q: Calculate each of the following given that: a. b. a-b a x (2b - 3c) |b x 3c| C. d. projac a = 2i -…

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Q: 4 [Lnce) - Lnce") dx

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Q: Solve this asap

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four…

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Q: y² = -25x 10- + the equation of the me focus is (Type an ordered pair. Type an integer or a…

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Q: f(x) ax² + B where x denotes the length of one side. Find a + ß. Your answer

A: We have given  fx=αx2+βx Put x=1 in fx f1=α12+β1 f1=α+β So, α+β=f1

Q: On the line y = 2x + 1, what value of Δy corresponds to Δx = 3? Δy =

A: y=2x+1 We have to find ∆y corresponding to ∆x=3.

Q: 3 (a) Find general solutions of the given differential equations: (i) y'"-6y' +9y = 0, (ii) y" - 6y'…

A: Note:-  As per your request i have done both sub parts of part (a)

Q: The graph of f(x) is shown (see figure). -7 (a) Find the following limits. L = lim f(x) = 2 Klim…

A: Concept: Limit of the function: Assume the function f(x). x should have values that are close to the…

Q: 6) Line y=x between x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a)…

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Q: 1.Use interval notation to determine f(x)

A: Concept: The graph of a function: The graph of a function is the set of all points (x,y) in the…

Q: Find the slope of the tangent line to the curve − 3x² + 2xy − 4y³ at the point (4, 1). - 44

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Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14

Q: For the linear function y = f(x) df dx a. Find at x = 8. ƒ'(8) = b. Find a formula for x = f-1(y).…

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Q: −5x – 5, f(x) = 2x² + 2x - 1, x < -1 x ≥ −1

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Q: The planets move around the sun in elliptical orbits with the sun at one focus. The point in the…

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: 5. Which of the following expresses √175 in simplest form ? a) 5√2 b) 5√7 c) 7√5 d) 9√5

A: Given that, the number is 175.

Q: If f(x) = 2x²-x+ 3, find the following. f(1) = f(-1) = f(a) = f(-a) = f(a + 1) = 2f(a) = f(2a) -…

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Q: Use the graph of the function to estimate the local maximum and the local minimum of the function.…

A: We have to use the graph of the function to estimate the local maximum and the local minimum of the…

Q: Suppose that p(t) is the growth rate of a population of bacteria at time t minutes. What does 15…

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Q: 2. What is the average rate of change between x = 2 and x = 3 for the function g(x) = 4(x + 1)² -5…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the length of the Arc length= curve r(t) = (71, 5, √¹4²) for -4 ≤ t ≤ 4. 2

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Q: QUESTION 4 Given the following function, find the values of f (5,2). x f(x,y) = 5 + xln(xy-9) O A.…

A: We can answer the question as below.

Q: sec x In the figure to the right, the equation of the solid curve is y= 2 dashed curve is y=2 cos2x.…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: y' + y = y²

A: Given: Now,           y' +y=y2⇒dyy2-y=dtIntegrating both sides we get,⇒y=11-et+c1

Q: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

A: Recall; sin2x+cos2x=1

Q: 1 lim x cos- #48 X lim 00-00 = lim 20-00 cos (1/x) 1/x [-sin (1/x)] (1/2) -1/x² =lim sin 22-00 = 0 1…

A: Here, to evaluate limx→∞x cos1x

Q: Given the ODE: dy dt - --(t-1) cos(y). 4(0)-3 Estimate y(1) using midpoint method, h=0.5. Present…

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Q: Given the function graphed below, evaluate the definite integrals. 4+ 3 2 1 -1 7 -1 -2 -3 -4 1 S.³…

A: Need to find out the definite integrals.

Q: Find the equation of the tangent line to y=−6/x^2 at x=−2. Write your answer in slope-intercept…

A: The equation of the curve is y = -6x2 To evaluate: The equation of the tangent line to the given…

Q: 2y dx + x(x² In y − 1) dy = 0.

A:

Q: Find the Riemann sum for f(x) = x² + 3x over the interval [0, 8] (see figure), where x₁ = 0, x₁ = 1,…

A: The given function fx=x2+3x over the interval 0,8 with x0=0, x1=1, x2=3, x3=7 and x4=8 Riemann sum:…

Q: (2x² + 2xy + y²) dx + (x² + 2xy - y²) dy = 0

A:

Q: . Find the equation of the parabola with x-intercepts -7 and 3, and that 2, -11). Express your…

A: Given parabola has two x-intercepts, (-7, 0) and (3, 0). Clearly its either upward or downward…

Q: 5. dy/dx = sin(x + y). ANS. x+c = tan (x + y). sec (x + y).

A: Please see the below picture for detailed solution.

Q: QUESTION 7 Evaluate the double integral. FS= 3xy 2 RX²+1 OA. 8 3 OB. 16ln (2) OC. 8ln (2) OD. 16 3…

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Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A: Please see the below picture.

Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: The given integral is ∫x3-6x-4dx Integral formulas, ∫xndx=xn+1n+1+C∫dx=x+C

Q: Which of the following is the correct limit definition for the derivative of g(x) = x² + x? O (x+h)²…

A: We have given function  gx=x2+x gx+h=x+h2+x+h Derivative of g(x) is given as  g'x=limh→0gx+h-gxh…