Rationalize the denominator, Express in simplest form. 5√3+ √2 2√3-√2

Q: lim f(x) = [Select] x-c function with nonzero denominator at x = c. for f any polynomial function or…

A: Given that,*f is a polynomial function or any rational function with nonzero denominator at x=c.We…

Q: Q1: Use logarithmic differentiation to find the derivative of the function = (cos (2x))x y =

A: Given Function is as follows As we know that

Q: 2. Identify the values of the variable for which √√4-x is defined. Show the values on a number line.

A: Given that the variable  we have to find identify the value

Q: A producer and distributor of gift cards produces a boxes of cards per day at an average cost 16x +…

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Q: Calculate the volume of the solid G bounded above by the sphere x² + y² + z² = 16 and below by cone…

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Q: The table below gives the population of a town (in thousands) from 2000 to 2008. What was the…

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Q: 2. Let P₁ be the plane 2: = 3x + 1, and let P₂ be the plane 6+y-4z=-3. (a) Find the acute angle…

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Q: sin cot-1 (2/20 CSC 2π 3

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Q: 4. Find the intersection of the two planes. T₁: X+ 2y+3z + 1 = 0 T₂: 3x + 2y +z+2 = 0

A: To find the intersection of the following two planes.

Q: Find a pair of numbers whose sum and product are both equal to 32. (Use symbolic notation and…

A: A pair of numbers whose sum and product are both equal to 32.

Q: Problem 2. Find the expected value and variance for the random variable X whose probability density…

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Q: Recall that the "leading term" of a polynomial is the entire term (including coefficient) containing…

A: The given polynomial functions

Q: Find the derivative of the function.   ​h(x)equals=left parenthesis x Superscript 8 Baseline minus…

A: The objective of this question is to find the derivative of the function h(x) = (x^8 - 1)^3. In…

Q: For the function, find the points on the graph at which the tangent line is horizontal. If none…

A: For the given function, to find the points on the graph at which the tangent line is horizontal.

Q: Give an expression for p (x) so the integral p(x) cos(7x) dx can be evaluated using integration by…

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Q: For the function, find the points on the graph at which the tangent line is horizontal. If none…

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Q: Find the linear approximation for f(x) Answer L(x) = -x+2/ = cos x at x =3/2

A: Linear approximation of f(x) at x=a is given by

Q: dy 2 + 3x²y = 6x² 2 dr.

A: To solve the following differential equation.

Q: Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle…

A: Solution is following in explanation step.

Q: Part 1: The First Derivative Find the open interval(s) on which f'(x) is positive / negative. Type…

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Q: Find the slope of the given line, if it is defined. (If an answer is undefined, enter UNDEFINED.) m…

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Q: For the​ function, find the points on the graph at which the tangent line is horizontal. If none​…

A: The objective of the question is to find the points on the graph of the function y=5x+1 where the…

Q: $₂ Use property 8 to estimate the value of the integral 10 8 10 8 ≤ s [ 0 = de s x dr.

A: By using the property 8 to estimate the value of the integral

Q: a) Solve homogeneous system of equations: quate so x'(t) = -6x (t) - 4y(t) y'(t)=-3x(t)- 10y(t)

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Q: lim_an= n→∞ an = √√√35+ 3n X

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Q: Given that f(t) = 5 sin(5t), find the average value of f(t) in the interval 2 <t<6, correct to two…

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Q: 1124 + 195812 +1592114

A: To find:-

Q: K Find the equation for the plane through Po(-6,4,5) perpendicular to the following line. x = -6+t,…

A: The objective of the question is to find the equation of a plane that passes through a given point…

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

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Q: 1 Use the graphing utility to plot the curve y = sin(x) and the horizontal lines y = 1 and y 2 (When…

A: The graph is shown below:The green line represents .The purple line represents .The curve represents…

Q: (c) 8 tan(x) < 8 sin(x) (ол Зл П

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Q: Evaluate each expression based on the following table. X f(x) (a) f(2)= f(-2) -3 -2 2 3 -101 5 3 -2…

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Q: (b) ∞ 2 X 2 2 (8x² - 12x) dx -∞

A: given integration

Q: Find b so that the points (3,-4), (4, −6), and (b, —2) lie on a line. b =

A: Let suppose three points are If the above three points are on a same line then

Q: 23. (1) the domain of f is (-∞0, 0] (ii) f(-2) = f(0) = 1 (iii) lim f(x) = +∞ --x

A: The given conditionsThe domain of f is (-]

Q: Find an equation of the plane that passes through the points (-3,1, 1), (0, 2, 3), and (1, 0,-1).…

A: Solution-

Q: Recall the point-slope formula for the equation of a line given its slope m and a point (a, b) on…

A: The objective of the question is to recall and explain the point-slope formula for the equation of a…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: For the solution follow the next steps.

Q: Find the intersection of the three planes. π₁: 2x + y -z +3=0 π₂: x-y + 2z = 0 π3: 3x+2y-z+5=0

A: To find the intersection of the following three planes.

Q: In three-space, find the distance between the skew lines: [x, y, z] = [1, −1, 1] + [3,0, 4] and [x,…

A: The skew lines The distance between skew lines is

Q: Directions: Construct a Regression Model for the following data. Year Wage (in dollars) 2000 5.15…

A: Given:U.S. Federal Minimum Wage with year To find:find regression modelpredict minimum wage for year…

Q: a) Solve Cauchy Problem: 2143 X- +2y=x+1 TO HATYI

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Q: How do you graph the ellipse? (x−2)² 81 Drag choices into the boxes to correctly complete the…

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Q: Graph the given equation. y = 3x+2 -x + 2 O No Solution -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10 O 8 7 6 5…

A: The given equation is

Q: surface area: an open rectangular box is to be 4 feet long and have a volume of 200 cubic feet. Find…

A: an open rectangular box is to be 4 feet long and have a volume of 200 cubic feet. Find the…

Q: 3. If three equal subdivisions of [0,3] are used, what is the Trapezoidal Rule approximation of…

A: Trapezoidal rule

Q: Let f(x)=-2x²-3x-5 and g(x)=√√x+14. Find the limits. lim g(f(x))

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Q: For the function f(x) given in the table, find the average rate of change over each specified…

A: For the function f(x)  given in the table, find the average rate of change over each specified…

Q: Evaluate the integral t S -8e³ sin(t-s) ds 0

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Q: (a)Show that the vectors a = 2i + 4j8k, b = 3i -j + 3k and c = -5i + 11j - 25k are coplanar.

A: Question No. (a): To show that the vectors are coplanar.Note: Since you have posted multiple…