For O x 1/2 -dx and using the substitution=x1/2, the resulting integral takes the form: -du du -du 4u 4-u² 4u - (21²) ² -du

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) c) is…

A: Concept: The equation of the line segment parallel to the given axis and passing through the point…

Q: (x - 3y + 3)dx + (3x + y + 9)dy = 0

A: On solving this we will get

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: To evaluate O fx²cos x²cosx dx' use integration by parts. What is the expression after the second…

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Q: x-5 X-3+x-3' 31. Determine the lim A. 0 B. -00 C. +∞ D. does not exist

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Q: Solve for the Partial Derivatives and total differential of each of the following function

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Q: Estimate the slope (slope rise/run) of the tangent line to the curve. N 3 4 6 N D-

A: topic- slope of a line

Q: rve (y+1)2 = 4x3 from x=0 to x=1? (4) =q8

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Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: π 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x==. 4 4 A…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2 x-x² if x ≤ 2 - Let f(x) = 2x - 1 if x > 2 Calculate the following limits. Enter "DNE" if the…

A: Let fx=2-x-x2 if x≤22x-1 if x>2To calculate the following limits. To enter "DNE" if the limit…

Q: 9 Determine the area to the right of g (y) = y² +4y-5 and to the left of the y-axis.

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Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: see below the answer and calculation

Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: 12

A: We will solve the problem.

Q: Ji 16 sin² x cos² x dx dx B

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

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Q: Suppose the consumption function for a particular country is c(x), where x is national disposable…

A: This question can be solved using the concept of differential equation.

Q: I co cos³ x sin x dx

A: Given problem:- ∫cos3(x) sin(x) dx

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

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Q: Use the quotient rule to find the derivative of the following. 2x-3 y= 7x+5

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Q: 5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+…

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Q: Use Cramer's rule to solve the systems in Problems 21-32. 21. 3x + 4y = 2 5x + 7y = 1 22. 5x + 8y =…

A: 22. The given equation is: 5x+8y=38x+13y=5 To use the Cramer's rule to solve the system of…

Q: A cheetah chase a deer which is 100 m ahead. The time in which the deer takes 10 leaps the cheetah…

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Q: "+9y' + 18y = 0

A: Topic:- application of derivatives

Q: m-1 1 + m 1 m m+2 ¹tan (+2)(x) + —tan" (x) + C m-1 1 + m 1 m+3 Ɔ+ (*) (1 - 1)² + (x) (1 + m) U²1-…

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Q: INALTIIX Large Drop-Fro... Summary - Qui... George Floyd: '... Paraphrasing T... when did geor...…

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Q: For the following exercises, find aj dt and direct substitution. 226. f(x, y) = x¹, x=t, y=t using…

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Q: N|- x² Given: quadric surface S with equation (y - 3)2 - 2 (a) Determine and identify the traces of…

A: Quadratic surface S with equation y-32-x22-z22=1

Q: If sin 20 = √3, 0≤ 20 ≤ 2π, calculate the values of

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: 19

A: We will solve the problem

Q: Evaluate Stan" (x) tan" (x) sec¹x dx

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Q: 47. Evaluate: x(x² + 3)5dx A. (x²+3)6 + C 12 B. (x²+3)6 + C C. ²/(x²+3)6 + C D. (x²+3)6 + C

A: According to the company rule we can answer the first question and rest can be reposted.

Q: ¡¡xaydx xexy dydx 10 Option 2 Option 1 e²+e=¹+3 e²+8²-3 e²-6-1-3 Option 3 None of the choices

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Q: Solve the following trigonometric equation for 0 ≤ 0 < 2π. Show your work. 4 cos²x 3 =

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Q: Question 6 6dx For the method of partial fractions, to evaluate S90 -1 = S Adx + S = X-1 Bdx X+1'…

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Q: 3. z = x+y x-y

A: The given function is  z=(x+y)/(x-y).

Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

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Q: For each of the following, state whether it has meaning. If not, explain why: (a) (ū. v) — |w| (b)…

A: We have to find the vector meaningfull

Q: Find the general solution of the ff.differential equations.1.)dy/dx=x+1/2(y+3) 2.)dy/dx=y^2(1+e^x)

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Q: (B) Find equations of the tangent and the normal lines to the curve y-exy = sinh x² +ln(x+√y point…

A: Given the curve y-exy=sinhx2+lnx+y at the point P0,1

Q: Integrate the following: 1. f xdx x²-x+1

A: The given integral is x/(x2-x+1). Repost the next question.

Q: Find the velocity of the particle at the times given. Velocity at time t = 1: -3 Velocity at time t…

A: We will find the velocity.

Q: WAN 1 2 3 4 The graphs of 4 functions are shown above, and the graphs of the derivatives of those…

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Q: dx x√x-1 dx √8+6x-9x² 3. S 4. S

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Q: C)Use LHospital's rule to evaluate only two of the following limits (if exist): 5⁰-6 lim (ii) lim…

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Q: Consider how we can evaluate this integral using u-substitution: x S dx. √2x+1 If we let u = 2x+1,…

A: This question can be solved by integration by substitution.