81.2² 18 3x-2 = For the rational function h(x) a. Find any intercepts of the function. State them as ordered pairs. find each of the following:

Q: 1+3 Sketch a detailed graph of the function g(x) asymptotes and draw them on the graph as dashed…

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Q: 018 Find the area of the region bounded by the polar curve r = 2e-0 as well as the rays 0 = 0 and 0…

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Q: X = 8 At the end of your work, sketch the graph of 5 x²¹ 2. y 8x8 and 1. y = 3. The tangent line at…

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Q: Find the general solution= y sin 2x tan² x y =

A: Given,Differential Equation y'y=sin2x.tan2x…

Q: Question 10 Determine the derivative of the given function y = log(a+b) cosh (2³) where a an…

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Q: Find Vectors and Perform Vector Operations in R³ Let à = i + 27 + 3k. Find ||a||.

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Q: Suppose that a population of bacteria triples every hour and starts with 300 bacteria. Find an…

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Q: 2. (x-2) y = y+2(x2) دعا 3

A: Given x-2y'=y+2x-23

Q: 2. lim (x, y)→(π/2,0) cos y + 1 y - sin x

A: Given query is to find the limit of the expression.

Q: Find the volume of the given solid. Diag 47 12 under the plane x - 2y + z = 5 and above the region…

A: The solid is under the plane is x - 2y + z = 5 and above the region bounded by x + y = 1 and x2 + y…

Q: 9 8- 7 16 1 A 3 يها 2 1 If f(x) f'(3) = = g(x) g(x) h(x)' 2 3 x-values then 5 4 يها 2 1 h(x) 1 2 3…

A: Given that graph of gx and hx    and fx=gxhxTo find :f'3Solution…

Q: Find the following using the table below. I f(x) 1 2 3 4 3 2 4 1 1 3 1 2 3 1 4 f'(x) 2 4 g(x) 4 3…

A: Given thatthe table To find :1. h'2 if hx=fx.gx2. h'2 if hx=fxgxSolution…

Q: Evaluate a multi-variable function Let f(x, y) = √√150 - 2x² – 4y², and evaluate f(1, 0). Please…

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Q: How do you get the exponent of 1.67?

A: Given solution :

Q: 3. The population of Sometown was 12,000 in 2000 and grew to 15,000 in 2010. Assume that the popu-…

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Q: Problem 1 Given a first-order differential equation: √1 + x² dy-ydx = 0 a) What is the best solution…

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Q: 4. y'-(3+anx)y = 1

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Q: A rectangular poster is to contain 162 square centimeters of print. The margins at the top and…

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Q: 22. lim (x, y)→(0,0) 1 - cos (xy) xy

A: See this solution in below.

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let x m be  length and y m be  width of rectangle  Perimeter of rectangle=2x+y m Area of…

Q: Horizontal Tangent There is a curve 3 y = x³ − 6x² + 12x + 5 What is the value of x where the curve…

A: Derivate y with respect to x and equate it to zero

Q: A series circuit has a resistance R = 10 Ohms and inductance L = 2. The battery gives a constant…

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Q: Write the equation: Vertical asymptote at x = −1, double zero at x = 2, y-intercept at (0, 2)

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Q: 1. Evaluate the integral f2162+12+0dx. (Hint. You may need to use partial fractions and trigono-…

A: Here we use the partial fraction to compute the integral . see below the answer and calculation we…

Q: e) y = √x4+7x

A: Solve for the derivative

Q: g(x) = 25x² (a) (¹) (b) (c) (d) 1 g(a) g(√a) ✓g(a) Additional Materials

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Q: Find the cross product axb 6=(-4,3-5) Where a= (-3, -5,0) and (483 axb = <D₁ 0₁ 02

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Q: Number 1: Given a first-order differential equation: /1 + x² dy − ydx = 0 A) Solve for the general…

A: Need to find out the solution of the differential equation.

Q: Calculate the consumer's surplus at unit price ō = 10 for the demand equation q=20 -0.05p²

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Q: The total spent on research and development by the federal government in the United States during…

A: Total spent on research S(t)=3.1ln(t)+22 billion dollars Total spent on in 2012    t= 12

Q: Find three positive numbers whose product is 86 such that the sum of their squares is as small as…

A: Let the three numbers be x, y and z. x + y + z = 86 -----(1) ⇒ z = 86 - x - y ------(2) Product, P =…

Q: Which one of the following could be the graph of the polar function r = sin 30 ? 1. 011 2.

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Q: Find the directional derivative Du f(−5/6,1) for the function f(x,y)=cos(π(3x+4y)) in the direction…

A: Given fx, y=-cosπ3x+4y v=9, 12

Q: f(x) = e* (tan x - x - x²)

A: We can find the derivative using product rule in the below steps.

Q: Question 29 Given 3x7 +825 - 21. determine, y' 630x +480x² + O 2520z³ +960x O 840x³ +360 P DE 126…

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Q: Write an equation (any form) for the quadratic graphed below 5+ y = 3 2 1 -5 -4 -3 -2 -1 + -2 -3 1 2…

A: Given query is to find the function of the graph.

Q: A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German…

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Q: Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

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Q: Consider the surface x² + y² - 2xy - x + 3y - z = 0 at the point Po(2, -3, 14). Determine the…

A: Concept: The equation of the tangent line at point x1,y1,z1 a(x-x1)+b(y-y1)+c(z-z1)=0 The symmetric…

Q: 4 Recall that the volume of a sphere is given by V = The radius of a spherical balloon is increasing…

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Q: 5. | tan’xsec*xdx

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Q: A bacteria sample initially has 300 organisms. After 2 hours there are 500. Write an equation that…

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Q: The volume of a box is 10x3 + 27x2 + 2x - 24 with the length 5x - 4 and the width 2x + 3. Find the…

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Q: Tutorial Exercise Find the derivative of the function. HINT [See Example 1(b).] h(x) In[(-3x + 7)(x…

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Q: Find an equation for the tangent plane to the surface 6 z + 2 = xy cos(z) at the point (2, 1, 0).…

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Q: Write the Parametric Equations of a Space Curve Find the vector equation that represents the curve…

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Q: Solvex - y = x² sinx dx Select one: O a y= cx? − xỉcosx O b. y = cx+xcosx O c. y = cx-xcosx Od. y=…

A: Topic = Differential equation Correct Option  = c

Q: Evaluate the double integral. 4y 1634², 0-{(x,x108281,0882²} D = {(x, y) 1 0 ≤ x ≤ 1,0 ≤ y ≤ x²} 5x5…

A: See this solution in below.

Q: Find the slope of the tangent line (10-x)y² = x³ at the given point (5, 5). Round your answer to two…

A: Derivate the given equation with respect to x