a²u əxəy ди dx = pt when x = 0, u = siny+ 3y² + 1 =e*cosy + 2xy when y = 0,

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the point (, ).…

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Q: Q9. For the following integration ſcos x² dx dy . 2 a. Sketch the region of integration.

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Q: Given the geometric sequence: 22, Find an explicit formula for an, where the first term is a₁ an =…

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Q: Simplify sin (80)+sin (40) cos (80) + cos (40) sin (80) + sin (40) cos (80)+cos (40) = (Simplify…

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Q: For what value of k will the function f(x)=x- k have a relative maximum at x = -8?

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Q: Find the volume of a solid bounded by z = 4 - y2 and the planes z = 0, x = 0, and x = y using…

A: According to question,Given Functions,z = 4-y2,and the planes z = 0, x = 0, and x = y.

Q: A cylindrical can is to have volume 2700 cubic centimeters. Determine the radius and the height…

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Q: 5. Determine the value of k for which f(x) = 4x² - kx + 6 has a horizontal t

A: Given: f(x) = 4x2 - kx + 6 The slope of horizontal tangent is equal to 0.

Q: Find the general solution to the differential equation y' which passes through the point (0, 3).. =…

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Q: Find the limit of f(x): lim f(x)= -2+ 8-1X 9- lim f(x)= X→∞0 (Type a simplified fraction.) 4 X (Type…

A: To evaluate: limx→∞fx and limx→-∞fx Given: fx=-2+3x9-4x2

Q: 4. Determine a. b. s'(t) s' (t) = 4t+ s'(t) = 4t+ for s(t) = 3t³+2+². Show your work. C. IN || d.…

A: According to question,Given Function,st = 3t13 + 2t2

Q: Find the orthogonal trajectory of the curves x ^ 2 = c *(y ^ 3)passing through (1,4).

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Q: Solve the given differential equation. e5x -5ydx-dy = 0

A: e5x-5ydx-dy=0 this can be written as  e5xdx = e5ydy now apply integration both side we get ∫e5xdx =…

Q: 1+ csc x cos x + cotx

A: Given query is to simplify the expression.

Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

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Q: Solve the differential equation. (Use C for any needed constant.) 5 + √r 6 + √u du dr

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Q: 6x. Using the formal limit definition of the derivative, prove that 3x² =

A: Using the formal limit definition of the derivative  we have to prove that derivative of 3x^2 is 6x.…

Q: Find the general solution to the system of ODE's x'= Ax, where -4-3 -1 - A =

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Q: Use the Divergence Theorem to evaluate J where S is the sphere x² + y² + z² = 1. (11x + 9y + z²) dS

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Q: X 16. Determine the equation of the tangent to the curve y=30* at the point with x-coordinate.

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Q: Find the derivative of: A) y = 2* B) y = 4x² +3

A: Topic:- application of derivatives

Q: Given the following data, calculate b, of the quadratic New difference polynomial: f(x)=0 f(x₁) =…

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Q: Use Calculus to find the behavior of g. g(x) = x³ 3x²is restricted to the intervalr € [1,4] 19. g(x)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: dy 15. Determine the derivative dx for y = 3 cos(8x+6) Show your work.

A: The function is given by y = 3cos8x+6 To evaluate: the expression of dydx.

Q: Sketch the domain D given by x < 0, y ≤0, x² + y² ≤ 9 and, using polar coordinates, compute [[³y…

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Q: b- day-22 dx3 2022 - 2 +2y = 3ex d²y dx

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Q: write the answer in 4 decimal places please

A: Topic:- application of derivatives

Q: If ln(z² – 8y) — z − y-2 and y(3) = 1, find y/(3) by implicit differentiation. (3) - An equation of…

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Q: Q)solve the following system of equation using cramer's rule 5x₁-2X₂ +3 X3₂ = 16 2X₁ +3X₂-5X3 = 2…

A: Given system of equation are5x1-2x2+3x3=162x1+3x2-5x3=24x1-5x2+6x3=7

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt

Q: The velocity v(t) of a sprinter on a straight track is shown in the graph below. s(7) = 22 v(t) s(9)…

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Q: A fisherman on a wharf 1.7 meters above the level of still water is pulling a rope tied to a boat at…

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Q: Angle is in standard position and (-4, 0) is a point on the terminal side of . What is the value of…

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Q: sin² 4y dy

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Q: d dt (2D-1)x+ Dy = et 3Dx + (2D + 1)y = t If D= find a complete solution of:

A: Let's solve given differential equation.

Q: 3. R is the region between f(x)=xln(x) and the x-axis on the interval [1, e]. (a) Write an integral…

A: Since you have posted multipart question i can do first three subparts as per our company guidelines…

Q: f(x, y, z) = x² + 3xy − z² + 2y + z + 4, Po(0, 0, 0), v=i+j+ k

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Q: a B cos (A): = tan (A) Note: Triangle may not be drawn to scale. Suppose a 10 and b = 9. Find an…

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Q: A frog at point A on the shore of a circular lake wants to reach point B diametrically opposite A.…

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Q: For the sequence defined by: a1 = 2 an+1 = Find: a2 a3 Jottam CHIESCHRE a4= 5 - +4 an

A: According to question,Given Sequence,a1 = 2,an+1 = 5an + 4

Q: Find the average value over the given interval. y=4e-x; [0,4]

A: Given query is to find average value of the function.

Q: 9) The sequence a₁ = a) Diverges b) Convergest c) Converges to 15 2 d) None of the above 4n²+1

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Q: Find the area of the largest rectangle that can be bounded by the positive coordinate axes and the…

A: To find the area of the largest rectangle that can be bounded by the positivecoordinate axes and the…

Q: A man wishes to use 141 feet of fencing to enclose a rectangular garden. Determine the maximum…

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Q: 245 students enrolled in a freshman-level chemistry class. By the end of the semester, 6 times the…

A: Let the number of students which failed be x.

Q: 9. Find the derivative of A) B) y = (lnx)4 y = ln x4

A: we know that  lnxn=nlnx dlnxdx=1xA)   given   y=(lnx)4

Q: Evaluate the indefinite integral (10-20x) a 20x¹) csc²(2x³ - 5x) dx For the toolbar, press ALT+F10…

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Q: Evaluate the integral. [x³√√x² +1dx

A: To evaluate the given integral

Q: Find how fast the volume of a parallelepiped is increasing if its edges a, b, and c change at rates…

A: According to question,Given Data,edge of parallelopiped,a=3 units,b=10 units,c=6 units,andRate of…

Q: Sketch the region enclosed by y = e³, y = e¹x, and x = 1. Find the area of the region.

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