1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

Q: 6. (2y²x−y) dx + x dy = 0

A: 6. 2y2x-ydx+xdy=0 Note:     Multiple questions are given, we are answer with only one question. If…

Q: dy dx Q5: Find for the following functions: (2) y = tan³√√cot(7x);

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 3 cos(t)i…

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Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

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Q: Q5: Find for the following functions: dx (4) y = x sinh 2x-cosh 2x (3) y = e* sin² x In√x

A: See this solution in below

Q: Consider lim (x,y) → (0, 0) xy 20 X (see figure). 20 20 (a) Determine (if possible) the limit along…

A: Here to determine, lim(x,y)→(0,0)x2+y2xy

Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: Skill Building In Problems 13-24, use the graph on the right of the function f. 13. Is fincreasing…

A: Please see the answers below.

Q: 3. (x³+xy²-y)dx + (y³+x²y+x)dy =0

A: We need to find the solution for (x3+xy2-y)dx+(y3+x2y+x)dy=0

Q: Think back to early in the semester when the weather was cold and often snowy. Imagine that in a…

A: Concept: Here we have the height of the mound is 24 inches (h) And the base of the mound is 36…

Q: | dx X æ /æ2+100

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Q: Determine where the vector function r(t) = i + (14t) j is continuous. Use symbolic notation and…

A: Please see the below picture for detailed solution.

Q: Describe the domain and range of the function. g(x, y) = x√y

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Q: X y = x + Ae^ + Be - 2x

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Q: k [[ x=0&y=0 x cos(xy) dydx =

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Q: √ grams/cm² and occupies Find the mass and the center of mass of the lamina with density 8(x, y)=-…

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Q: Find the distance between the pair of points (2.5,8.2) and (-0.5,5.2). If necessary, express the…

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Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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Q: A polynomial function g(x) has a negative leading coefficient. Certain values of g(x) are given in…

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Q: (a) Find S 1+ (x + 2)² dx and 1+ (x + 2)² dx.

A: Concept: Integration: The summing of Discrete Data is indicated by Integration. To determine the…

Q: Q / if w = tan x and x=4²++ Find dw dt

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

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Q: 5. Find the volume of the solid by the shell method. The solid is obtained by rotating the region…

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Q: Q2: Solve the following f (1) 7x² +14+15 (x²+3)(x+7) dx :

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

Q: Q5: Find dx for the following functions: (1) xcinh 2x coch 2x (3) y = e* sin² x In√x

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Q: 8 If f(x) = 3 + = + x 6 x2 find f'(x). Find f'(4). Round to 3 decimal places if necessary.

A: Given that f(x)=3+8x+6x2-(i)Our Aim is to find f'(x) and f'(4).

Q: y"+y=t y'(0) = -2 y(0) = 1

A: The differential equation is given by      y'' + y = tThe auxiliary equation of the corresponding…

Q: Find the unit tangent vector T(t). r(t) = t²i + tj +4k, P(9, 3, 4) TO) (No Docpopcol

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Q: Using the Factor Theorem, which of the following is a factor of the polynomial function f(x) = 5x² +…

A: Given polynomial function is f(x)=5x3+5x2-60x

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;

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Q: 2. y(x4-y²)dx + x(x++y²)dy = 0

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Q: S 2 (2x² + 1) dx

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Q: Q5: Find for the following functions: dy dx (4) y = x sinh 2x - cosh 2x

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Q: 2. 3. ત્ર 6 -1 cos²2x dx X - dx

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Q: 2. Evaluate the following: t² dt a.

A: To solve: ∫−11 t2t2−62dt Let I = ∫−11 t2t2−62dt since,  t2t2−62 is an even function  Therefore, I =…

Q: doesn't this mean there are no critical points

A: Given the function fx,y=10x2-5y2

Q: Describe the domain and range of the function. F(x, y) = 5x² - y Domain: 0 {(x, y); x = 0} 0 ○ {(x,…

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Q: 28. For each of the following equations, find the most general function N(x, y) so that the equation…

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.012 per…

A: Given data÷ Marginal cost  cp=$0.012 per page  Where p=number of pages

Q: Given f(x) = - 12√x + fractions. f'(x) = The domain of f'(x) is 20 X 18, find f'(x) and its domain…

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Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n = 10 over the…

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Q: (B): If A = 2i + 3j-4k; B = 3i-4j+ 5k and C = i + j-k, find: (iv) (3A + 4B). C (1) A.B (U) B.C (iii)…

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Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Compute the indefinite integral of the following function. r(t) = (13 cost,7 cos 5t,3 sin 6t)

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7.

A: I have stated the used formulas in the solution

Q: A circular swimming pool has a diameter of 16 ft, the sides are 6 ft high, and the depth of the…

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Q: Q3: Evaluate the following integrate: (chose three only) 1. dx 1+x4 2. ex-edx ex+e-x 3. fxsec² x dx…

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Q: Use the limit definition of partial derivatives to find fx(x, y) and fy(x, y). f(x, y) = x2 − 4xy +…

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Q: 10.¹ (3x² - y²) dx + (xy − x³y¯¹) dy = 0 2 du

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Q: Find a differential equation whose general solution is 8t y = c₁est + c₂e-2t. = 0

A: We can find the differential equation as below.