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Q: Continuity At what points of ℝ2 are the following functions continuous?

A: Given: f(x,y)=x2+y2xy2-1

Q: Is the limit of f(x) as x approaches c always equal to f(c)? Why or why not?

A: The function fx approaches fc from left and right both then the function is said to have the limit f...

Q: Factor: 2x3 + 8x2 + 8x.

A: We have to factorize the algebraic expression: 2x3+8x2+8x Taking '2x' common from the terms, we get ...

Q: Prove the following equivalence. Show each step of your proof. rv기r→s)r

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Q: Evaluate the limits.

A: As per the bartleby guidelines for more than one part only only one has to be solved. Please upload ...

Q: NOTE: Solve this as soon as possible, I need this urgently. Find the gradient vector, tangent plane ...

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Q: 2. 4 9. 10 11 12 13 x -1+ 2- -3+ -4+ -5 6- (2,-6) (12,-6) The graph of y = f(x) consists of a semici...

A: Giveny=fx consists of semicircle with end points 2,−6 and 12,−6To find∫212fxdx

Q: 1 For the following parametric equation x(t) = tan t and y(t) = sec t find the tangent line passing ...

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Q: Fill in the blank/s: Determine whether the sequence 4, 8, 12, 16, 20, . . . is arithmetic or geometr...

A: Given: 4,8,12,16,20.....

Q: What is the mass density 8(x, y, z) of a solid of volume 5 m3 with uniform mass density and total ma...

A: Given - Volume of the solid = 5 m3Total mass of the solid = 25 kgFormula for finding the mass densit...

Q: Find the equation of the bisectiors of the obtuse angle between the lines x + y - 5 =0 and x – 7y + ...

A: The given equations are  x+y-5=0 and x-7y+7=0. Then, a1a2+b1b2=11+1-7=1-7=-6≤0 Therefore, the obtuse...

Q: Evaluate the integral. inegral 1  to 2 [(4 y2 -7y -12 )/ y (y+2)(y-3) ]dy

A: Given:                  ∫124y2-7y-12y(y+2)(y-3)dy   To determine:                    We can solve us...

Q: Including 8% sales tax, an inn charges $162 per night. Find the inn’s nightly cost before the tax is...

A: Let the inn's nightly cost is $x. Including 8% sales tax on it the charge becomes $162.

Q: Find a function that models the area A of an equilateral triangle in terms of the length x of one of...

A: We know the height (h) of an equilateral triangle with the length x of one of its sides is: A = [(sq...

Q: Use the given vectors v = 5i, w = j to find v.w and v.v

A: Given :             vectors   v = 5 i  + 0 j         and    w = 0 i + 1 j          Formula:      If ...

Q: find the first and second derivatives w = 3z7 - 7z3 + 21z2

A:   Given the function, w = 3z7- 7z3 + 21z2 Differentiating with respect to "z" dwdz = w'=37z6-7(3)z2+...

Q: Convert the angle 300° in degrees to radians. Express your answer as a multiple of π.

A: To convert the angle 300° in degrees to radians.

Q: Find the complex fifth roots of -1 - i. Write roots in rectangular form.

A: Lets assume, z=-1-i

Q: Find the exact value of the trigonometric function cos 9π/4 . Do not use a calculator.

A: We have to find exact value of the trigonometric function: cos 9π4 Rewriting the given trigonometric...

Q: Use Squeeze Theorem to evaluate lim x→∞ (cos x/ x)

A: It is known that the absolute value of the cosine function is not greater than 1, hence -1x≤cosxx≤1x

Q: Graph the function P(x) = (x - 2) (x - 5) (x -4)  and find all local extrema, correct to the nearest...

A: Given, Px=x-2x-5x-4 Px=x-2x-5x-4        =x2-7x+10x-4        =x3-4x2-7x2+28x+10x-40        =x3-11x2...

Q: 1 4. lim 2t-1 t-

A: Note:- We will answer the 4th question since we answer only one question at a time. Please submit a ...

Q: Consider the function f(x) = 4x° 4x on the interval [ – 5, 5]. Find the average or mean slope of the...

A: Given  f(x) = 4x3-4x on interval [-5,5]   Mean slope = [f(b) - f(a)]/(b-a)

Q: Find each limit, if it exists.

A: (a) limx→∞ 3-2x3x3-1=limx→∞ x3x-2x3x2-1x=limx→∞ 3x-23x2-1x=0-2∞-0=0 Thus, limx→∞ 3-2x3x3-1=0.

Q: Calculus Question

A: Since you have asked multiple questions in a single request, we would be answering only the first qu...

Q: Fill in each blank so that the resulting statement is true.

A: Given that: r1cosθ1+isinθ1r2cosθ2+isinθ2

Q: Sketch a graph and determine the area of the region bounded by y=2x^2+10 , y=4x+16, x=2 , and x=5.

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Q: Find the equation dy/dx +Py=Qyn where P and Q are Functions of x

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Q: Graph the curves y = x2 - (x3/6)

A: The given equation is y=x2-x36.

Q: Evaluate ∫sin3 x dx by splitting off a factor of sin x, rewriting sin2 x in terms of cos x, and usin...

A: the given integral is: ∫sin3x dx we have to evaluate the given integral by splitting off a factor of...

Q: Solve the logarithmic equation ln(x - 4) + ln(x + 1) = ln(x - 8). Be sure toreject any value of x th...

A: Given:  ln(x - 4) + ln(x + 1) = ln(x - 8)

Q: If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2? Explain your reaso...

A: Given f(2) = 4 Then we get, we cannot precisely say that, "As x tends to 2, f(x) approaches zero."  

Q: Consider the function f(x) = 2x – 6x? slope of the function on this interval. 48x + 7 on the interva...

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Q: Determine the convergence or divergence of the series

A: Known fact: If limn→∞ an ≠0  then ∑n=1∞ an diverges.  

Q: Determine the amplitude, period, and phase shift of the function. Then graph one period of the funct...

A: Given that: The equation is y=3 sin 2x-π2 .  

Q: Use logarithmic differentiation to find dy/dx. y = √[x2(x + 1)(x + 2)], x > 0

A: Given, y=x2x+1x+2, x>0  

Q: Find the volume of the solid of revolution formed by rotating the region bounded by the x- axis, the...

A: Given x=y2 ,x=y find the volume of the solid about y- axis  

Q: What are parametric equations?

A: Parametric equations are the functions in which both the variables x  &  y are defined using a t...

Q: 3 Reindex the series E so that it starts at k = 1. k=5 4k- - 63

A: Given  The series is ∑k=5∞34k2-63 .

Q: Please help me as soon as possgible

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Q: Calculate the area enclosed by y=sin x, y=cos x and x/pie for each of the following  intervals: a) ...

A: our objective is to find the area under the curve

Q: b) Use L'Hopital's rule to find the limit: 1/In x (In xv lim

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Q: I am not sure how to do this question.

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Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane ...

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or (x,y,z)=0,0,2+t1,1,3+s2,0,-3⇒x=t+2s...

Q: Determine whether the given relation is a function. Give the domain and range for each relation. (se...

A: The domain of a function is the set of all possible inputs for the function. Here, the input value i...

Q: Find the equation of the tangent and normal to the following corce at the points indicated against  ...

A:

Q: Find r′(t), r(t0), and r′(t0) for the given value of t0 = /2. Then sketch the curve represented by t...

A:                                                      r( t ) = 3 sin t  i→+ 4 cos t  j→r( t0 ) = 3 si...

Q: Simplify : (5x - 7)(3x - 2) - (4x - 5)(6x - 1).

A: Given : (5x-7)(3x-2)-(4x-5)(6x-1)

Q: Find the following limit. t2 + 5t – 36 t – 4 lim t+4

A: First, we have to find the limit limt→43t2-1t-5. limt→43t2-1t-5=3(4)2-1(4)-5=48-4-5=39 Now, find the...

Q: The table below shows selected values for a continuous function g over the interval 2,6]. 2.5 3 3.5 ...

A: The given table is,  

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.