The traffic flow rate (cars per hour) across an intersection is r(t) = 500 + 600t – 120t2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 8 am?

Q: x3 + x2 – 5x + 15 dx 5. (x2 + 5)(x² + 2x + 3)

A: Partial fraction: A complicated rational statement is decomposed into two or simpler fractions using…

Q: For f(x)=3xv(4-x²) determir within its domain..

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Q: 1+x dx V1-x

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Q: Find the slope of the function f(x) = V5x at x = 5. V5/2 -25/2 1/2

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Q: Problem #2: Differentiate f(x) = [(2x3 – 8)(5x² – 3x – 9)]° and solve f'(2). Solution: Reason:

A: The given function,      f(x)=2x3-85x2-3x-93

Q: 4 about the point a = 3. (Your answers should include the variable x when appropriate.) Find the…

A:

Q: Find the equation of the tangent line at the given value of x on the curve. 3 4 2y° + xy - y =…

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Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: Here we have to find relative maximum ,mininmum points and saddle points.

Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: Exercise 1. Find the following limits 2 3x + tan 2x 2x + x tan 2x sin 1) lim 2) lim 5x +x tan 2x 3)…

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Q: (1) (2) (4) B" A" A" B" 90 B'

A: We will find the type of pairs of lines.

Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: ANOTHER A baseball team plays in a stadium that holds 52,000 spectators. With ticket prices at $10,…

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Q: Evaluate the summation (2i - 1)? - i=1 155 162 165

A: Topic = Algebra

Q: 00 n2+9 E(-1)"-1 n2+ 8 n=1 a) Show that the ratio test fails b) Test the given series for…

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Q: Use the like-bases property and exponents to solve the equation n-2 () = 23n +5 > Next Question

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Q: Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity…

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Q: 1. For the curve x²y? = 25 at (-1,-5), find the equation of the normal line. %3D

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Q: -6- They" for y = -9 3x-5

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Q: = a and log5 2 = b then log5 216 can be expressed as pa + gb. The value of (nearest whole number)…

A:

Q: Solve the given VSDE dy/x − y (dx/x^2) = 0

A: Solution: As per given data,  dy/x − y (dx/x^2) = 0 we solve by variable separable method In that…

Q: The integral 4x dx Vx2 – 4 1 is an improper integral of typel is an improper integral of type II…

A: The given problem is solved below in detail.

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: 1. f(г) — 2? + Зх — 6, д(х) %3 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Evaluate the following integrals. 4x545 2. 3. fx Vr? - 4dx 4. S(2- sin 4r) dr

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly re-post other…

Q: Problem #2: Differentiate f(x) = [(4x³ – 1)(8x² + 6x – 3)]° and solve f'(2). %3D Solution: Reason:

A: To differentiate the given function.

Q: The count in a bateria culture was 800 after 10 minutes and 1000 after 35 minutes. Assuming the cou…

A: Given

Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

A:

Q: Compute the partial derivatives: ,2 z = In(x² + y³) az dy

A: Use partial derivative

Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 - f(x) %3D (x3 –…

A:

Q: Consider the parabola given by the equation: f(x) = 4x° – 10x + 2 Find the following for this…

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Q: 1. (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its…

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Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: Using appropriate trigonometric substitution, dx xV4 - x2 is transformed to 1 S csc 0 de cos e d0 2…

A: Topic = Integration

Q: 2x+3 (a) Given f(x) = and g(x) = , determine (g f 1-x

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: x = -1 x = 1 For what value of c is the function f (x) = continuous at x = -1? 12 –1 (x+1)(x-3)…

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Q: Draw a right triangle containing 0, so that the opposite side is 2, the adjacent side is 5, and the…

A: Topic:- trigonometry ratios  Note :- as per our guideline if more than one question uploaded than…

Q: Given that f(x) = x² - 5x + 6, evaluate the function fla +b) - fla). 2a+b-5 b-5 2a+b+1

A: Simplify the expression for the given value of x

Q: If a series Σ an n=1 is convergent, then it is absolutely convergent.

A: 1)∑n=1∞ an is convergent,then the series may not be convergent.for example, an is alernating…

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: | 4.5x + 3.2y = 7.7 0.8y 0.9x 0.1

A:

Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Sx² sec² x³ dx .2

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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Q: Problem #2: Differentiate f(x) = [(3x* – 5)(2x³ + 9x – 6)]° and solve f '(2). Solution: Reason:

A: Solve the following

Q: Consider this function: y=-5 sin(3x+x) (Continued from previous question.) Imagine the graph of this…

A: We will find the 5 points.