Exercises: Find the derivatives of: 1. 1-y = (secx + tanx)(secx- tanx) 2- y = x2.cotx- x2 4. 1+cscx 4-y = 1-cScx

Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

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Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 18x + 2…

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Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 7…

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Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

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Q: Solve the initial value problemy-10y +50v-0 for y(0)-1 andy (0)-5. After getting the equation for…

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Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x?2 - х) dx x2 + x +1

A: ∫01x2-xx2+x+1dxit is a improper fraction ( degree of Numerator= Degree of denominator)Using long…

Q: Find the area of the region enclosed by the parabolas y=x and y=2x-x². Make a sketch and shade in…

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Q: On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric…

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Q: Find all first and second partial derivatives of the following function: f (x, y) = e*Y + y sin x.…

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Q: x* +x² 5. lim,-. e* +1

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: A company manufactures rope, and the total cost of producing r feet of rope is Cr dollars.To…

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: cos(2x)– cosx sin x 4. lim, »o

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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: 3 da Evaluate a+2 A. 3 B. 2 С. 1 D. 0

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Q: A cylindrical water tank 8 meters high with a radius of 2 meters is buried so that the top of the…

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Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ),v(PR), and v(PS) respectively 31…

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Q: Describe the graph of the equation. r = 10 cos ti + 8 sin tj – k O It is an ellipse in the z = – 1…

A: Given that       r = 10 cost i + 8 sint j - k

Q: Use Hooke's Law to determine the work done by the vaniable force in the spring problem. A force of 7…

A: The answer is 5.6 pounds

Q: (4x-3) find dy/dх y = (2х-7)6

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Q: Consider the function y-2+3x² -x³ a) Find the intervals on which this Punction is increasing or…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point (2,…

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: k S = (d – 2)? where c and k are positive constants which depend on the quantity of smoke each stack…

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Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x²…

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Q: Find div F and curl F if F(x, y, z) = 10y°2³i – 11x°z!°j – 3xy°k. „10: div F= curl F=

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Q: What is the second derivative of f(x) 2x-3 2 x+1 10 (x+1)* 10 3 (x+1)° -10x+10 (x+1)* 10x-10 (x+1)*

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Q: Find the four second partial derivatives, Observe that the second mixed partials a z = 19xeY-10ye

A: We will differentiate partially with respect to x and y.

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: Evaluate the integral / (2x + 9y)dx + (6x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: Find the derivative of the following equation: (2x – 1) (3a? + 2) - O 48x + 36x2 + 22x + 8 48x3…

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Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0, 0). %3D…

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

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Q: (1+x, if x 2 %3D

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Q: dy Solve the differential equation = -3 cos x-4x if y(7)=0. dx

A: To solve the given differential equation.

Q: Describe the domain and range of the function. KX, y) = 9x2 - y

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Q: Let F(t) = * F(e)dt (dont include the «C) Fine Question Help: D Video Add Work

A: We know, ∫tndt=tn+1n+1 ∫-sin-tdt=∫ddt-cos-t=-cos(-t)

Q: r In x 2

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Q: ||r(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). r(t) = t'i + tốj K(t) =

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Q: 2. Find an equation of the plane containing the point P (0,-.) and the line determined by the two…

A: Equation of a plane P containing a line of intersection of two planes P1,P2 is given by, P=P1+λP2

Q: Evaluate the definite integral (cos(t), sin(t))dt

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