cos-¹ Q6A)If y cos = prove Zyy + z = 0. B) Z = (1 + i)(2-1)-¹, find |21. 倉

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3x F(x) = [ cos (tº) dt.

A: Here we use fundamental theorem of calculus.

Q: 3 1. f ³√x² dx

A: Solution : Given that integral is

Q: 15. Show that the equation, ³ + e* = 0 has exactly one real root.

A: we have x3+ex =0to check number of roots we can draw graph of both and check number of intersection

Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: y=-3 √9-y² |25−x − y’ dxdy=

A: The given double integral:∫y=-3y=3∫x=-9-y2x=9-y225-x2-y2dxdyWe need to evaluate the above integral.

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y =…

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Q: he line integral of the vector field F= over the curve C which is the quarter of the rcle from…

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Q: 10. S xdx (5x2+3)4

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Q: The graph of the second derivative f" (x) is given below. On what interval(s) is the function f(x)…

A: Solution

Q: Is the function has a extreme point? If yes, Locate the extreme point: 1 + 3x V4+5x2 y

A: Find derivative of function and equate to zero to find critical points

Q: 2x et. Vi-eza ex fer.

A: ∫ ex1-e2xdx=∫1-u2du=∫1+cos2v2dv=12·∫ 1+cos2vdv=12∫…

Q: Apply the rule of integration by parts. -S Sudv. dv = uv - du = Let dv= ew dw and integrate the…

A: Here we will fill all blacks of prat 2 as shown below

Q: I. Use the definition of the Laplace transform, using improper integrals, to find the Laplace…

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Q: 29 + i√/1159 6

A: We can convert the given complex number in fractional form to decimal form by calculating the square…

Q: Part 2. Integration by substitution Solve the following integrals through video presentation. √x+1 x…

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Q: Represent the plane curve by a vector-valued function y=1-x^2

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Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

Q: 3 5. S (t + ²1) ²³ dt t

A: To evaluate the integral.

Q: Find the amplitude, period, and phase shift of the function. =I 1 sin (3x-x)+3 Give the exact…

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Q: 38. A rectangle is inscribed in a semicircle with diameter 10 centimeters as shown. Express the area…

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Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: Solve the given IVP using Laplace transforms. x" - 2x + x = 2tet x(0) = 0, x'(0) = 0

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Q: Find r'(t), r(t0), and r'(t0) for the given value of t0. Then sketch the space curve represented by…

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Q: Solve the given differential equation by undetermined coefficients. y" + 5y = -180x²e5x y(x) =

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Q: Find the minimum rate of change of f(x, y) – y³e-² at the point (0. — 2).

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Q: Find the function F that satisfies the following differential equation and initial conditions.…

A: This question is based on diffrentiation equation and solved using Laplace transform.

Q: 4 Determine -2 u tv and Give a is i and v и So Keat orthogonal to ²-5²³ lutô| = |a²|+12²1…

A: Given the vectors u+v and u-v are orthogonal and  u+v=u+v To find u and v .

Q: Determine whether the set, together with the indicated operations, is a vector space. If it is not,…

A: We have to choose correct option.

Q: Consider the following situation, which involves two options. Determine which option is less…

A: To find out which one is less expensive.

Q: No calculators. Find the exact length of the curve. 0≤x≤l y=2+2x³/2,

A: Length of the curve  =∫ab 1+f'(x)2 dx .

Q: Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20…

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Step 2 Apply the rule of integration by parts. J u dv = uv - Submit J Let dv = ew dw and integrate…

A: topic- indefinite integral

Q: Let f be a function given in the graph below. Note that the domain of f is [-3, 4]. a) Does f have…

A: Given the graph of a function. To determine whether the function has an inverse on the given…

Q: 17. Assume that f'(x) = (x - 1)(x - 2)²(x-3)³. (a) Find the interval(s) on which is increasing. (b)…

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Q: Use the formula for the binomial series: (1 + x) = to obtain the Maclaurin series for 1 (1 + x)5° 1…

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Q: Using [ y = e^(2x) (c1 + c2) + 3/2x2 (2x) ] and [ y = ( c1 + c2x ) e^(2x) + 3x/25 sinx + 4x/25 cnx +…

A: The given differential equation is;  y'' - 4y' + 4y = 3e2x + xsinx

Q: Find the critical points of the given function. 5. f(x) = 2/3+2/3 +x-2/3 6. f(x) Va 7. f(x) (3x +…

A: Given: 5)     fx=14x43+x13+x-23 After simplifying we get     fx=14x43+x13+1x23 Critical points:…

Q: xdx

A:

Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: we have given the graph of f(x) we know that at maxima and minima f'(x) =0  (means slope at that…

Q: Given r(t)=t2i+5tj, find and completely simplify T(t) and N (t)

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

Q: Solve the differential equation by variation of parameters. 3y" 6y' + 6y = ex sec x y(x) =

A: We have to solve the differential equation.

Q: Determine whether the series is convergent or divergent. 00 Σ M = 3 n-0.9999

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Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: Prove that for any integer n if 3n+ 2 is even, then n is also even.

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 150 Find the consumers' surplus for a product if the demand function is given by D(x) = 3+x Answer…

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Q: Define f by f(x,y) = ["h(t) where h is some continuous function of one variable such that h(0) h(1)…

A: We have to solve above question.

Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: Switch the order of integration of the following integrals, then evaluate: ƒ ƒ x sin(y²) dydx = x=0…

A: Explained below