1. Evaluate each limit: lim x+5 3x x² +1

Q: (A) f(x) = √√√x + 2x (B) f(x) = √√√x – 2x² (C) f(x) = 2x² + √x (D) f(x) = 2x − √√x

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A: Given a cardboard of size 30 inches by 30 inches, after cutting out squares of size x by x from each…

Q: Question 1. Let f(x) = (x³ + x² + 1)e²³+1 and g(x) = e³+1. (a) Draw a rough sketch of the graphs of…

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Q: Given the following relation between x and y answer the following questions. a) Using implicit…

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Q: Find the area of the region bounded by on the interval [1,8] f(x) = e4x and g(x) = 2x 2x on

A: The area of the region bounded by the curves y= f(x)  and y=g(x) on [a,b) is given by

Q: You have been given the following system of linear differential equations: z' = 14x + 16y, y = -12z…

A: We solve the given system of linear differential equations using the method of elimination.

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A: To determine the producer surplus at the market equilibrium point, we first need to find the…

Q: Using integration by parts, the integral f (sin-¹ x) dx becomes IT 12 +2 # ( So² da dz So T 12- Soda…

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Q: Find the volume of the solid graduated by revolving the area bounded by the given curves about the…

A: Given that ,find the volume of the solid by revolving the area about .

Q: Use Laplace Transforms to find the solution to the initial value problem y′ − 3y = u1(t)((t − 1) +…

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Q: +'? + Lo 3 2 14 -2- for q The function graphed above is: Increasing on the interval(s) Decreasing on…

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Q: Solve the initial value problem: y'+4y= 0 y(3) = 100 y(t) =

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Q: Compute In (7x) x4 S dx.

A: given integration

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Q: 1 Find the arclength of the curve x = 3 Y 1 t² with 1 ≤t≤ 2. 2

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Q: U.S. Online Video Viewers The number of online video viewers in the United States was growing at the…

A: The number of online video viewers in the United States was growing at the rate ofr(t)=9.045e0.067t…

Q: 16. A solid generated by revolving the region bounded by the curve yine and the lines = 1, e about…

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Q: x(t) = (t +3)² − 4; y(t) = (t + 3) traces an ellipse. a parabola. O a circle. O a line. O a…

A: According to bartleby guidelines we supposed to do the first three sub parts of multiple sub parts…

Q: Find the average value of the function over the given interval. y=5-x²: [-1, 1] O A. 413 О в. о 14

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Q: 6. Find GCF (156, 24) and LCM (156, 24)

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Q: a. Select the correct choice below and fill in the answer boxes to complete your choice. O A. f(x) =…

A: We need to fill in the boxes.

Q: by (0) -31 13 A cylindrical 3 m³/min. How

A: Let radius of the cylinder is denotes by r Let height of the cylinder denotes by h Then volume of…

Q: Evaluate Lyds, y ds, C: x = t², y=t, −2<t<5

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

Q: Find the area of the shaded region. 6 4. 2- -2- -4- -6- y=x-1 2 3 v=x²-4x+3 2 4 5 to 6 X

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Q: (b) Find the rate at which the depth of water is changing when h=10 cm.

A: Given that,vertical height = 25cm, water depth = h cm. From the given figure (a) Since, the volume…

Q: Use the given function and the given interval to complete parts a and b. f(x)=2x³-24x²+72x on [1,7]…

A: NOTE: Refresh your page if you can't see any equations..The given polynomial function is,The given…

Q: Evaluate the indefinite integral: Su ² (G√0 + √√ ) du

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Q: 7 For the function f(x) = x³ + 3x² find the following (Show your work) (a) Intervals of…

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Q: π.χ. COS(TEX) 3 f(x) = 7 cos

A: f(x)=7cos⁡(πx3)

Q: Convert the rectangular equation x² - xy + y² = 3 to the polar coordinates 3 2-sin 0 Or= o po² = =…

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Q: Using the Law of Sines to solve for all possible triangles if ZB = 50°, a = 106, b = 45. If no…

A: As we know that Angle sum of a triangle is 180Formula for the sine law is given as

Q: Which statement is true about the infinite series It is absolutely convergent 1 In 2 + In 3 1 In 4…

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Q: J F. dr. (Check the orientation of the curve before applying the theorem.) F(x, y) = (²x + x²y, e²y…

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Q: Compute fx²³ In (8x) dx a) = 6 x + [+\n (8x)=1] + C 4 b)x+ [4\n(8x) +1] +C c) = x²4 [4Ln (8x) + 1] +…

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Q: 1 (sec hr)2 1+tan ha 6 B=? +0 B e² +1 da = A + ln- (sec hx)² dx = Apen B e²et letanhx

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Q: Using separation of variables, solve the differential equation, Use C to represent the arbitrary…

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Q: Using the derivative of f(x) given below, determine the critical points of f(x). f'(x)=(x + 5)(x+2)…

A: By using the derivative of  given below to determine the critical points of .

Q: Consider two functions f and g on [3,9] such that [f(x)dx= a. 5 S71(x)dx= 7f(x)dx= 28 (Simplify your…

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Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

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Q: Evaluate fy'da – a³dy, where C'is the boundary of C the region between the circles x² + y² = 4 and…

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Q: Consider the vector field F= (2x + 3y, 5x + 2y) Is this vector field Conservative? Select an answer…

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Q: If sin(x) = = sin (2x) = 9 20 (in Quadrant-I), find (Please enter answer accurate to 4 decimal…

A: Trigonometric Formula

Q: Use linear approximation, i.e. the tangent line, to approximate 4.66 as follows: Let ƒ(x) = x³. Find…

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Q: Use series to expand and evaluate the limit

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Q: 15 The velocity function (in m/s) of a particle moving along a line is given by v(t) = 3t 5. Find…

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Q: Evaluate طرحة (Inx)³ X -dx

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Q: Question 2 A kite, 30m high, is being carried away horizontally by the wind at the rate of 10m/s.…

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Q: 14 Find the point (s) on the ellipse 4x² + y² = 4 that are farthest from (1,0). (Show your work)

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Q: T Specify a sequence of transformations for the function h(x) = sin x + of h from the graph of the…

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Q: Solve the following differential equations of 1- yy' = 2y - x; 2-(x-y)

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