2. Evaluate the following integrals a) f √1+2-√1-dx (Hint: Maybe you need to rationalize the fraction!) √1+x+√1-x

Q: Find all values of where the graph of f(x) = 2x³-39x² + 240x-5 has a horizontal tangent line.…

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Q: 1. 7. What is mos(+h)- cos(2), ? h (A)-1 (B) - √2 2 (C) 0 (D) 1 (E) The limit does not exist. 2 If…

A: 1 limh→0 (cos(π/2 +h) -cos(π/2))/h limh→0 sinh/h - 0 this is formula so answer  = 1 answer D is…

Q: A ladder 15 ft long leans against a vertical wall. If the lower end is being moved away from the…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(4, 2, 4),…

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Q: 4. A company's average variable costs are given by a function 0,202-7Q + 150. Find out where the…

A: Given Average Cost :- FQ=0.2Q2-7Q+150

Q: Evaluate the limit: lim x-6 x² + x - 30 x + 6

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Q: 10. xy dx (x + 2) dy = 0.

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Q: If F(x) = 5x/(1+ x2), find F'(2) and use it to find an equation of the tangent line to the curve y =…

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Q: III. Eliminate the arbitrary constants of y = c₁ cos3x + c₂sin3x.

A: Given function, y=C1cos(3x)+C2sin(3x)

Q: If y = √4x²+2sin-¹ A. 2-x 2+x A. 0 B. 2+x 2-x ,then y' equals, C. . Find d if y = arcsin√2x +…

A: Topic- Derivative of a function we are given y=4-x2+2sin-1x2and y=arcsin2x+arccos2xwe know…

Q: Find the equation of the plane passing through the points O=(0,0,0), A=(−4,5,1)and B=(−1,0,−6)

A: plane passing through the points O=(0,0,0), A=(−4,5,1)and B=(−1,0,−6)   that is plane passing…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) […

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Q: For the polynomial, one zero is given. Find all others. 4) P(x) = x3 - 7x2 + 15x - 25; 5

A: NOTE: Refresh your page if you can't see any equations. . the given root is x=5 so take the…

Q: 7x4-12x²+5=0 71x1² 110

A: 7x4-12x2+5=0 by hit and trial method clearly x=1, -1 is the root of the above polynomial equation.…

Q: Solve the Initial = Find the general valve problem jy (0) = -1 solution (x² + 1) + 3xy =6x

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Q: dw dt = x²y = xy³, x = cos(t), y = et Find: @t= 0, when w =

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Q: - IV. Solve the VSDE (x² − 3)dx + xydy = 0.

A: Topic = Differential equation

Q: Find y' of tan(x²y4) = 3x + y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative on both sides

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

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Q: Using the attatched equation 3.9, find the general solution of the following differential equation…

A: Given data:- The given differential equation is, dy+2xy-xe-x2dx=0

Q: Solve the integrals: (1) (c I₁ = 1 |x| x² + x| dx

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Q: Michael and Jennifer are arguing about a graphing question where they are required to determine the…

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Q: Find zxand zyif z = x² tan¯¹ (²) — y² tan¯

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Q: A differential equation (DE) is a mathematical equation for an unknown function that relates the…

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Q: 9²-9 9² + 69 79 2 9²-29-3 9² +29-3 2

A: To simplify ans solve the given question

Q: If a force of 49 N stretches a spring 0.7 m beyond its natural length, how much work does it take to…

A: We have given  Force = 49 N Using Hook's law F=kx ........(i) k=Fx Put F=49 N and x = 0.7 m k=490.7…

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

Q: Element X has a half-life of 10 days. If we currently have a 25 ounce sample of Element X, how long…

A: NOTE: Refresh your page if you can't see any equations. . the half-life of the element X is p=10…

Q: A rectangular piece of land has dimensions 1050 ft by 550 ft. Find the area of the land to be…

A: The length of the rectangular land, l = 1050 ft Width of the land, w = 550 ft To evaluate: The area…

Q: A. A. Find if x = 2t4 - 4t² and y = t4 - 4t. dx t²-t+1 2t(t+1) B. t² +t+1 2t(t+1) Find f'(t) if f(t)…

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Q: Qe Evaluate the following integrals, then reverse the integration order 2 c2x 1) (4x + 2)dy dx.

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Q: At the beginning of the year 1995, the population of Townsville was 3312. By the beginning of the…

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Q: 2x Find the second derivative of y = e²x sin(3x)

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Q: Use an appropriate table of values to find lim h->0 b^h-1/h where b = 48, accurate to four…

A: The given limit limh→0bh-1h We need to find the limit for b=48

Q: 3. Verify Clairaut's Theorem on by showing fry=fyx. f(x, y) = 4 x² + y² + 2

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Q: II. Show that y = C₁e²x₁ C₁e²x + c₂e³x is a solution to the DE y" - 5y' + 6y = 0.

A: Find the roots of the DE and then use them in the general solution.

Q: If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is…

A: We have to find the velocity when t = 1 second.

Q: Graph the function and identify intervals on which the function is increasing, decreasing, or…

A: In order to find range we have to check for maxima and minima

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: The given integral is sqrt(5+1/x)/x2.

Q: Evaluate the integral. 6 t² sin(2t) dt

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Q: Consider f(x)=5x-3-41/x^2 c) Find the equatino of the tangent line at x = 2 to the graph of y =…

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Q: Determine the solution of the 1st Ordered Differential Equa 3(x² + y²)dx + x(x² + 3y² + 6y)dy = when…

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Q: If A is the matrix below compute A4. Be sure to use trigonometric identities to simplify so that the…

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Q: Find f=V 3 √x + y 6 02 f дудх

A: The given function is: fx,y=x3+y6   As we know that; The Chain rule: fgx'=f'gx·g'x The Power law:…

Q: QUESTION 1 Determine the solution of the 1st Ordered Differential Equation: xy³ dx + ye dy = e-*dy

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Q: B. 10/3 square units

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Q: Use PMT= 3¬ to determine the regular payment amount, rounded to the nearest dollar. The price of…

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Q: Evaluate lim A. dne 3x³-4x²+1 A. R x-00-7x³+x2+2 B. 0 C. - 31/12 The domain of y = log(1-2x) is B.…

A: Givenlimx→∞3x5-4x2+1-7x5+x2+2 We have to find the value of the limit of the function And we have to…

Q: Apply Newton's Method to approximate the x-value of the indicated point of intersection of the two…

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Q: The hypotenuse of a right triangle is twice as long as the shorter leg. x. Let y be the longer leg.…

A: Given x is the length lf the shorter leg, y is the length of the longer length. So, length of…