Given: zi = 2215° evaluate z and express the result in the Cartesian form. (Answer: j64)

Q: r(x) = 5 log4 (3x + 10)

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Q: (-2,5,7) + t(-3, 1,-4) and that the point Given a line defined by the equation T = P(x, y, 15) lies…

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Q: A hotel rents rooms to customers by the night. The hotel determines that if it sets the price of the…

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Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

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Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: 6. y dy 1+√√y √

A: The given integral,        ∫y dy1+y

Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F =…

A: Here, the given vector field is: F=x2i+5xj+z2k⇒curl F=ijk∂∂x∂∂y∂∂zx25xz2…

Q: With a curve 56 3 17 x² + y = 6, y = x, y = -2 and x = -2. . Determine its area.

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Q: It is known that for a function f(x), f'(1) = 0 and f" (1) = -0.5. What does the Second Derivative…

A: This question can be solved using the concept of second derivative test.

Q: Use the chain rule to find where st the pieces: z = x²y + xy², x=3-t³, y=3-t6

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Q: You deposit $2000 in an account with 4% annual compound interest. Complete the following, assuming…

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Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: 25- A) Use series to express the function f(x) = coshx.

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Q: Find the general and Singular Solution o the Following differential equation yLny = xyP+ P²

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Q: Graph two full periods of the function f(x)=cos(4x) and state the amplitude and period.

A: Given problem:- Graph two full periods of the function f(x)=cos(4x) and state the amplitude and…

Q: Find dy/dx, if y= (3+cos x) ^(2x+1)

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Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: Solve the equation: (D² - 4) (D+2) y = 0 Oy=c₁e²x + c₂x²x + c3e-²x Oy=ce+exe + c3e

A: To solve the given differential equation.

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A: The risk-reward function,    y=xlnx-2y=units of reward, x=units of risk

Q: Inys 5. lim y→⁰⁰ y

A: To solve for the limits of the following function using L'hospital's rule.limy→∞ ln y5y

Q: Three vectors u, v, and w exist such that - + = 0. Determine the value of ū+uw + (-). w, given that…

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Q: Find the equation of the family of curves having the given slope, and the equation of the curve of…

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Q: Determine the x - y coordinates of the points where the parametric equation x = 5 sin²t y = 2 cost 0…

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Q: (a) Find the dimensions of a box with a square base with volume 125 and the minimal surface area.…

A: According to our guidelines, In case of multiple questions, we are supposed to answer the first…

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: Question 8 A manufacturer has determined that the total cost C of operating a factory is C = 0.5 x²…

A: At what level of production will be average cost per unit

Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: 1) If y = (x-a)√2ax-x² + a² sin-¹(*), then y' = 2√/2ax - x² a a is constant. 2) If f(k)= k√a²-k² +…

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Q: 2)dy - ydx = 0 (x + y cot ) dy

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Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Please refer to the image below

Q: Evaluate 0-2²-²4 where is a unit cele centered at the origin

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Q: Calculus Use the Table of Integrals to evaluate the integral. 1₁ 21²6 2t²e-t dt

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: et (e2t + 8et + 7)² 3 dt

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Q: Determine if the function is continuous on the given interval. - 1. f(x) = √x² – 25 ; [−6, −5] 2.…

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Q: 100 (e) Σ199 2i(i3 – 1) i=1

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Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

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Q: Find the linear approximation of the function g(x) = 1 + x at a = 0. g(x) * Use it to approximate…

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Q: 26. *2# 70 x² sin x dx

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Q: The bacteria in a certain culture increase according to dN/dt = 0.25N. If originally N = 200, find N…

A: Integrate the equation.

Q: n Express the function n, lim 21³ n→+∞ n5 i=1 and then find the limit. in closed form

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Q: 11. Given f(x, y) = 6r² - 2r³ + 3y² + 6ry. Determine any local maxima, local minima, and saddle…

A: To find out the local maxima, local minima and saddle points.

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: Find the area of the region bounded by the curves y = x² and y = -x² + 4x.

A: Here we have to find the area bounded by the curves.

Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, the rate of change of revenue after the sale of x calculator: R'(x)=(x+5)ln(x+5)

Q: A. Find the derivative of each of the following functions. 5. f(x)=3x5 +6x² +9x 6. f(x)=2x² - 4x¹…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: Now find the area bounded by y= x^3, x=0, and y=3 a) 3.25 b) 3.28 c) 3.26 d) 3.27 integral…

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Q: 6. csch x dx

A: To find the integral of the given function.