What is the gradient of f(x, y) = x² - y4 at the point (5, 2)? O 5i + 16j O -15i-16j O -6i + 13j O 10i - 32j

Q: A trader buy's 80 mangoes. she finds that 8 are bad and a further 22 are unripe ,show on a pie chart…

A: Given data:- Total number of mangoes = 80 Bad mangoes = 8 Unripe mangoes = 22

Q: 2. (2xy-tan y) dx + (x²-x sec² y) dy Answer: x²y - x x tan y = C. = 0

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Q: Find all points of inflection and discuss the concavity of f(x) = x^2 *(3x - 5)^1/3

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Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s)} = f(t)g(t). O True O…

A: The given data is: Lft=Fs and Lgt=Gs, then L-1FsGs=ftgt is true or false.

Q: Find f such that f′(x)=8x​, ​ f(4​)=47.

A: Given, f′(x)=8x​,​ f(4​)=47.

Q: Your answer is correct. Find a differential equation whose general solution is = = C₁e⁹t + c₂e-³t.

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Q: Find a power series for the function, centered at c. 8 5-x £( n = 0 f(x) = C = 1 Determine the…

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y+3y" - 3y - 2y = et,…

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Q: 6 5 4 3 a The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 * ¹{2 ² - S 2

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Q: Given: f(t) = 3t4 + 6. Evaluate: F(3) Use 2 decimal places. 2.30

A: Here we have to apply laplace transform.

Q: If a rock is dropped from a height of 237 ft, its poistion t seconds after it is dropped until it…

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Q: Fill in the blank. (Enter your answer in terms of t.) 1 e-{2}- L²s² + n²π² 2_2

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Q: Give the Particular Solution of the following Differential Equation d²y 3 +2 dx² IBC: y(0) = 2 y'(0)…

A: The given differential equation is: 3d2ydx2+2dydx-8y=0 So, we can also write as; 3D2+2D-8y=0   The…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Given,           ℒ-11s2+1s2+25

Q: Determine whether the differential equation (8x² - 2xy + 2) dx + (7y² - x² + 8) dy = 0 is exact. If…

A: To solve the given differential equation

Q: Which if the following is a power series representation of the function - 1+x? f(x) = = +∞ Σ(-x" -…

A: Given: function f(x)=-1+x1-xwe know that11-x=1+x+x2+x3+..........=∑xn0∞where…

Q: etermine whether the equation is exact. If it is exact, find the solution. 2e³ycosy + 1² С 2e¹ycosy-…

A: We have to find solutions

Q: Find the critical numbers of the function f(x) = -x55x¹ +5x³ answers to three decimal places. X = X…

A: Given,            fx=-x5-5x4+5x3-9To find : Find the critical numbers of the function

Q: 2. sin x siny dy + cos x cos y dx = x² sin x cos y dx

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Q: y' = 4+t-y, y(0) = 1 (a) Find approximate values of the solution of the given initial value problem…

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Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

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Q: State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 2y = cos x Determine…

A: The objective of the question is determine the order and check the linearity.

Q: Find div F and curl F if F(x, y, z) = xz¹i+ 4ya²j+6z²yk. div F= curl F=

A: Vector

Q: Given

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Q: 1. By eliminating the parameter t from the following parametric equations, find an equa- tion in…

A: As per the instruction, we will be answering the first one. For (a), Given: Now,…

Q: enshot (1603) Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx −…

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Q: Consider the function f(x) Find the value of A: A = - 6x² + 6x 5. f(x) has a critical point at x =…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r = 4 cos 0 -…

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Q: Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)? Focus…

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Q: Fill in the blank. (Enter your answer in terms of t.) [ L-1) 1 5²-2) =

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Q: Find the general solution of the given second-order differential equation. 5y" + y = 0

A: To solve the given differential equation.

Q: A firm faces a marginal cost (MC) function: MC = 50 - 10Q+Q² (where Q represents units of output).…

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Q: Differentiate from first principle y = 5x²³² +22² +32 +4

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Q: • . 19

A: the equation of ellipse is given  below

Q: V -6 -5 -4 -3 -2 7 Submit Question 8+ gut 7 916104324 -6- -1 -2 -3- 4 --$ 166 46- U 1 2 4 5 Find an…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

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Q: Given: f(t) = 8 t 2 Evaluate: F(2) Round-off answer to 2 decimal places.

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Q: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: Use the Laplace transform to solve the given initial-value problem. y"" + 2y" y' - 2y = sin(4t),…

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Q: 1 x5 10 (266)6 This can be transformed into a basic integral by letting Consider the definite…

A: Given query is to transform the integral using substitution.

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: If two objects travel through space along two different curves, it is often important to know…

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Q: Mark the critical points on the following graph. 2²e-², 6,0.3 34 2.7 2.4 2.1 1.8 1.5 1.2 0.9 10.6 Q3…

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Q: Find both first partial derivatives. h(x, y) = e(x¹0 + 10 hx(x, y) = h₂(x, y) =

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Q: Find div F if F(x, y, z) = (x² + y)i + z² j + (ey - z) k. O 2x - 1 O 2xy - 1 O 2xi-k O 2xy i+ k

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Q: Answer true or false. The function f(t) = (et)10 is of exponential order. O True O False

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Q: V. (VXF) =

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Q: Given AB www. BA= and [2 1 2 2], find AB and BA. Hint: Matrices need to be entered as [(elements of…

A: The answer is given below:

Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

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