Exercises 7 Evaluate: 2 (2x - 3)* dx 5 (2) J 1 dx 0*+3 (3) dx x + 9 x In x dx

Q: Consider the function f (x) = - 3x³/% Which one of the following is true? O a) f is decreasing when…

A: If f'(x) > 0 for all x in an interval I, then f(x) is increasing over I. If f'(x) < 0 for all…

Q: Find an equation for a parabola with focus (– 10, 7) and directrix x = - 6

A: Find the equations for a parabola with focus (-10,7) and directrix x=-6.     Here i attached the…

Q: Estimate cos(π/4 - 0.1) + cosπ/4

A: Solving

Q: 1. Find an equation for a parabola with focus (– 10, 7) and directrix x = - 6.

A: A detailed solution is given below

Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

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Q: Find all the values of t where the tangent line to the parametric curve is horizontal or vertical.…

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Q: Find out whether the series given below converges or diverges. 00 Σ 3n +4 n= 1 Choose the correct…

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Q: 8. Let 7 (t) = < - 2 cos(8t),- %3D Find fF(t)dt (don't include the +C) frona -

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Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x х2-16 2. lim x-4 (Vx+5)-3

A: Given; (1). limx→07xsin2x

Q: Evaluate. (Be sure to check by differentiatingl) 1 dx, x# - 3 9+ 3x

A: To evaluate: I=∫19+3xdx Use the rule: ∫1xdx=ln |x|+C

Q: Determine whether the function is one-to-one. {(2,6). (3,9). (– 7,3), (1, – 5)} Is the function…

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Q: Find the consumer's and producer's surplus if for a product D(x) = 43 – 5x and S(x) = 20 + 2x .…

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Q: e slope of the surface z = int (2. 3) is xy² in the x-direction at the and the slope of this surface…

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Q: Determine whether the integral is improper (x-4) -'dx A Improper B Not improper

A: Given data÷

Q: Obtain the general solution for the following differential equation. (a) y" – (a + ß)y' + aßy = 0 (a…

A: To solve the given higher order differential equation.

Q: Solve e2x + 7e*+6= 0 Show every step.

A: We have to find the value of x according to the given information

Q: Show that (1-)" =e= %3D Which of the series converge and which diverge. 4n+3 (1) E=14 m%3D1 (-4)"…

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Q: When a factory operates from 6 AM to 6 PM, Its total fuel consumptlon varies according to the…

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Q: :Q2 Find F(t) for the differential equation below x²y' + 2xy – 2y = 0

A: We have to find the solution of differential equation.

Q: An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a line…

A: Let us sketch the situation roughly using these following information: N = North, S = South, E =…

Q: B. Solve the following problems using differentials and linear approximations. Show complete…

A: Let's find.

Q: point C on land such than ZCAB = 44.2°. Find the distance across the lake from A to B. В 506 ft…

A: Given the query is to find the distance between A and B.

Q: 5. Fill in the blank: For x, y ER. Equality in the Triangle inequality is satisfied, i.e. Ix+yl =…

A: x+y=x+ysquare on both the sides;(x+y)2=(x+y)2 x2+2xy+y2 =x2 +2xy+y22xy=2xyxy=xyis true only…

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A: Given that the population of mosquitoes in a certain increases at a rate proportional to the current…

Q: Using shell method, find the volume generated by revolving the area bounded by y = 2x – x2 ; y = 0 ;…

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Q: Determine whether the integral is improper (x- 4) -'dx

A: Step 1: Identify whether one or both of the bounds is infinite. If so, then this is a Type I…

Q: The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

A: Given: The radius of a sphere is increased from 20cm to 20.2cm. To find: Estimate the change in…

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

A: Given problem:- Find exactly T(t) and N(t) for x = et cost, y = et sint, z = et for t = 0

Q: 2. Rule 1: Subtract 4 starting from 20. Rule 2: Subtract 3 starting from 20. Sequence 1 Sequence 2…

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Q: dy Find dx of æ³ – y? = 5 by implicit - differentiation and evaluate the derivative at this point:…

A: According to our guidelines, we can answer only one question or three subparts of a question, other…

Q: Q4) Find for the following functions ( dx 3x+4 5. y = 2x+3 6. y = tan-1 V4x3 – 3

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Q: 5. , (6x2 – 3x + 5)d.

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Q: 5. a) Find the equation of any tangent(s) to the graph of f (x) = -x² + 6x + 5 that also go through…

A: Given

Q: Given that i = and i = and that i • v = 188 determine the value of the constant A.

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Q: dy I# 2x²y° - 3ry = at the point (1, 2)? 4x. what is %3D da O b) 2/3 O c) None of these O d) -43 e)…

A: Explanation of the answer is as follows

Q: When a factory operates from 6 AM to 6 PM, Its total fuel consumption varies according to the…

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Q: On each interval, determine whether the graph of f(x) is concave up or concave down. From x=1 to…

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Q: Given that u= and v= and that u.v= 199 determine the value of the constant A. Answer:

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Q: Find the area of the shaded region Blank 1 Note: Enter exact answer x = y 20 1000 y? 20

A: x=yx=1000y2Solve both the equationsy=1000y2y3=1000y=10The limits of y are from 10 to 20.

Q: Determine the value of 3A+1OB if 14x2 + 33x + 9 Cx + B %3D (x – 1)(x+ 1)2 x - 1 (x + 1)2 Answer:

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Q: A. Identify if the given limit is NORMAL, OSL-RIGHT, OSL-LEFT or DNE. x-2 1. lim x--4 x2-2x x+4 2.…

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Q: 3. Sx Vx? – 4dx 4. S(2 – sin 4r) dr 5. S cos x sin? x dx

A: LetI=∫xx2-43dxPut x2-4=udifferentiate 2xdx=duxdx=du2I=∫xx2-43dx.I=∫u32duTake the constant out:…

Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý - y = e*

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Q: Find an equation of the tangent to the curve at the given point. x = 8 sin(t), y = t2 +t, (0, 0)…

A: The given curve,x=8 sin(t), y=t2+t at (0,0)

Q: 3) A homeowner wants to plant a rectangular garden next to the fence in their backyard. The fence…

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Q: is xZ dz dx dy

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Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x?…

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Q: 3. The radius of a sphere is increased from 20 cm to 20.2 cm. Estimate the change in volume.

A: First write the volume of a sphere and then diffrenciate it and put all the values.

Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

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