Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

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Q: e same overtime Create Workflow xb₂) 5(21 @ (1) The volume of the solid obtained by rotating the…

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Q: lim (sech 2x)csch x x² +0+*

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Q: 1 sinh x cosh3 x √9-cosh² x dx

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Q: The population of a municipality in the country varies according to the function…

A: Topic:- Algebra

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: There are two 12-hour clocks, Clock A and Clock B. One clock is broken and it runs at a different…

A: Concept: There are two clocks A and B, one clock is broken and another one is normal which means…

Q: Q1/ Without using L'Hopital rule, find the following limit. √2+x-√2-x lim- ×-0

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Q: For several weeks, MMDA has been recording the speed of freeway traffic in EDSA. The data suggest…

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Q: Does the Rolle's Theorem applies for f(z) – ln(2 – z²) over the interval [−1, 1]? O Cannot be…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: What is the answer? Show your complete answer (with a graph) in a given-required-solution

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Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

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Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: First we draw the graph,

Q: You are given the polar curve r = 3 cos(0). (a) List all of the points (r, 0) where the tangent line…

A: We have to find the point for horizontal and vertical tangent lines.

Q: shortcuts

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Q: If y₁(x)=e³x and y₂(x)=xe³* are solutions to y" - 6y' +9y = 0, what is the general solution?

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Q: 312-3x| dx

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Q: Below you are given six polar equations and plots of four of these curves. Match each plot with the…

A: Consider the curves

Q: Find the area of the region bounded by the curves y = the x-axis using vertical strip. (x+1)2 y = 4…

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Q: The derivative of y with respect to a given ¹ = 1 is Oy' = yx²-¹ O y'= 0 Onone of the choices Oy' =…

A: I have stated the used formula in the solution.

Q: Solve the differential equation dx 4x+6y+5 - dy 3y+2x+4

A: Concept: The general form of non-homogeneous differential equation  dydx=a1x+b1y+c1a2x+b2y+c2 Check…

Q: 4. Find the area of the region bounded by the horizontal strip. y² +1 and the y-axis using

A: Topic = Area

Q: Evaluate the indefinite integral given below. (10 (10-20x4) csc² (2x³ - 5x) dx

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Q: Determine the values of r for which the differential equation ty"-5ty' + 5y = 0 has solutions of the…

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Q: The fixed-points of f(x) = (x² + 2) a¹ are 3 and

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Q: Show that (x+2)² = ln(x + 2) - x+2 + C.

A: Topic = Integration

Q: ૩ 3* sech³ (3) 1+tanh (3) S- -dx

A: Substitution method in integration: To simplify the integral, in the given integral independent…

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: Point of inflection is the point where f''(x)=0 A function is concave up in the interval (a,b) if…

Q: Write the first five terms of the sequence, give the exact answer: {n+13) n=1 Determine whether the…

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Q: Find the area of the region bounded by the curves 1 y = , y = 4 and the x-axis using vertical strip.…

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Q: Evaluate the indefinite integral given below using the indicated substitution. 1-20 -2(-2x + 9)³ dx…

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Q: Determine the instantaneous rate of change of the function √ sin sin (2³) f(x) = [x² x3 At x=1 dt…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

A: topic- inflection points and concavity

Q: Write z, and z₂ in polar form. (Express 8 in radians. Let 0 ≤ 8 < 2m.) Z₁ = 4√3-41, 2₂ = -1 +/ Л 2₁…

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: Evaluate the limit using L'Hôpital's Rule. 8x³ lim x-0 sin(x) - x (Use symbols and fractions where…

A: we want to determine the value of limit limx→0 8x3sinx -x

Q: Use Cartesian coordinates to evaluate y²2 dV D where D is the tetrahedron in the first octant…

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Q: Which of the following functions will be continuous on (0, 3)? OA. h() = 12 8² + 6| OB. g() = 7/2-16…

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Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: Find the area of the region bounded by 2x = and the y-axis using the horizontal strip. 4 y²+1

A: We have to find the area using horizontal strip.

Q: 1. Evaluate the integral: 2³ cos (dt du

A: Given

Q: The function g is continuous on the closed interval [1, 4] with g(1) = 5 and g(4) = 8. Of the…

A: This question can be solved using the concept of Mean Value Theorem.

Q: hat is the concave up and concave down?

A: In terms of the second derivative Concave Up, Concave Down, Points of Inflection,  The graph of y =…

Q: 1. Evaluate the assigned limit using L'Hopital's Rule. lim [cos (2x)]¹/(*-*) 2--

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Q: An integrating factor for the linear differential equation y' + = x is Select the correct answer. O…

A: This question can be solved using the concept of linear differential equation. Note: elna=a

Q: Determine Ex=1(-3)^-² its sum. O 4/7 5/7 O 7/2 7/4 the series converges and if so, find whether

A: On solving this we will get

Q: In a frequency table, the upper boundary of each class interval has a constant ratio to the lower…

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Q: integral: 2² sin (-) dt du Evaluate the integral:

A: use substitution method and integration of parts for solving the integral

Q: 1. Let f(x) = sin²(x) cos(x) g(x) = sin² (x) cos² (x) h(x) = sin² (x) cos³ (x) ㅠ (a) Plot all three…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: e2x 1. Evaluate the indefinite integral -1 dx. ex-1

A: