1. Basic Integration a. fx(x + 1)dx b. S √ √x+x² dx x C. √₁²|x-1|dx

Q: If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: 45-46 Find az/ax and az/ay. = = f(x) + g(y) 45. (a) z (b) Z = f(x + y)

A: We have to slove above questions

Q: 28. y² dx + (x² + 3xy + 4y²) dy = 0; when x = 2, y = 1. ANS 462v + y) ln v. 2 v

A: See this solution in below.

Q: The temperature T at a point (x, y) is T(x, y) and is measured using the Celsius scale. A fly crawls…

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Q: Calculate the 3 × 3 determinant. (Use symbolic notation and fractions where needed.) -2 6 -5 2 7 2 2…

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Q: The graphs of y = f(x) (solid) and y = g(x) (dashed) are shown. The two graphs intersect at (5, 18).…

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Q: At what points is the function y= x+3 2 xỉ - 5x+6 continuous? Describe the set of x-values where the…

A: We can find the x-values where the function is continuous in the below steps.

Q: b) For the curve 2² - 4ry² = y³ +9, do the following:

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Q: 4. Use implicit differentiation on these. a) Find an expression for dy/dx at any point on the curve…

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Q: Can you explain and show me how to solve this problem for applications of the integral: x = (1/2)y,…

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Q: ttt 1. lem f(x) = X-7-0 2. lim f(x)= x →∞ 3₁ f(8) = 4. f(-2) = 5. lem +(x)= X90+ 6. lem f(x)= 7. lim…

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Q: Suppose that a function f(x) is defined for all real values of x except at x = c. Can anything be…

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Q: (cos x-cosy-cotx) dx - sinxsiny dy=

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Q: Evaluate the integral dx ✔ -x+8x-12 0 dx 2 -x+8x-12 &

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Q: 5x²-19x+3 (x-2)(x+1)

A: To resolve the given expression into partial fraction the solution is as follow

Q: Find the solution of the given DE. dT 8. +0.0697=2.07; 7(0) = -30 dt

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Q: 3. Use grad h(-3,4)=5ī +3j and h(-3,4)=10 to answer the following questions. a) Find the…

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Q: 4. Use the graph to calculate the limits. You may assume that one square represents one unit on the…

A: Given graph of a function f(x)

Q: Find an equation of the sphere that passes through the point (3, 1, -3) and has center (1, 6, 5).

A: We use Distance formula between points x1,y1,z1 and x2,y2,z2⇒d=x2-x12+y2-y12+z2-z12

Q: lim x-2 2x² +1 3x-2

A: limx→22x2+13x-2

Q: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and…

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Q: 4. Let In = f cos" xdx. Show that: In = 1 - Cos' n on-1 x sin x + n-¹ In-2, n ≥2. n

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Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: Given that the graph of a derivative f' is shown to the right.

Q: Find the equation of the tangent line. cuberoot(7x-6) that is perpendicular to the line 12x+7y+2=0

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Q: Determine the dot product of (0, 5, 10) and (-3, 1, 0).

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Q: 3) h (x) = xcosx, at & 2

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Q: 25. (y + √√x² + y²) dx − x dy = 0; when x = √√√3, y = 1. ANS. x² = 2y + 1.

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Q: A particular curve passes through (1, 1) and satisfies the differ- ntial equation dx = (1-3y²³) dy.…

A: Let's find equation of curve in the form of x=h(y).

Q: Find the indefinite integral. (Use C for the constant of integration.) [sin³ sin³ 20 √ cos 20 de

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Q: Comparing Simple and Compound Interest 100 10 Use the slider to see what happens over time.…

A: For simple interest, the interest is earned only on the initial Principal amount(P) while for…

Q: A manufacturer produces bolts of a fabric with a fixed width. A quantity qq of this fabric (measured…

A: I am attaching image so that you understand each and every step.

Q: f(x)= 3x² 4 ln (x²)

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Q: Find the indefinite integral. (Use C for the constant of integration.) [si sin³ 20 √ cos 20 de [( 3…

A: Let's solve given integration.

Q: Find the area of the shaded region. 4 3 2 f(x)=x- 8x +21x, g(x)= -14x + 136

A: We can find the area of the shaded region using the required formula in the below steps.

Q: Find the area of the parallelogram determined by v = (2,0,0) and w = (0,-1,-4). (Use symbolic…

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Q: h(x) = (lx - 21 (4- 2x if x # 2 if x = 2

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Q: Find the solution of the given DE. 2. y' + 2xy = 2x³ ;y(0) = 1

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Q: Calculate y" and y". 8ex X y(x) = y" (x) = y"" (x) = [

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Q: QUESTION 4 Evaluate tan³3x dx 01 1 tan3x -x +C tan ³3x + C tan ³3x + C tan3x - x +C

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Q: Solve the inexact differential equation ydx + (2xy-e-2y) dy = 0.

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Q: 2. The height of a golf ball after t seconds is given by s(t) = 24t - 4.9t² meters. (a) Find the…

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Q: 1. Asymptotes at y = 5/3x - 29/3 and y = -5/3x + (11/3 and a vertex at (1, -3).

A: Given find intersection of asymptote , which is center of hyperbola ( h , k ) = ( 4 , -3 )   one…

Q: -3x Let G(x)=x2-9 A. Factor the denominator. B. State the domain of G(x). C. Determine the…

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Q: Find: i) fx³dx ii) f8y³ dy

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that:- Region bounded by y=lnx , y=1, y=2, x=0

Q: Sketch the parabola y = -x² + 7x + 18 and shade the area enclosed by the parabola and the x-axis.…

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Q: B. 3y² + 2xy = 8 dy dx m TL Equation of tangent line m. NL Equation of normal line

A: Given equation of curve:- 3y2+2xy=8

Q: Maximize f(x, y) = √11-x² - y², x + y - 2 = 0.

A: The given function to maximize is: f(x,y)=11-x2-y2 with the constraint g(x,y)=x+y-2=0...(1)

Q: 8) Given two planes P₁:2x+4y+3z=4 and P₂:x-y-2z=-3 (a) Let L be the line of intersection of the two…

A: Given Planes :- P1: 2x+4y+3z=4 P2: x-y-2z=-3

Q: lim x-2 2x² +1 3x - 2

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