Work all problems on your own paper, neatly and stapled with this worksheet/answer sheet. Y 1. f(x) = x² – 2x – 8 a) Standard Form: y = a(x-h)2+k V=ICx=)9 b) Vertex (pôint form): -9) c) Opens Up/Down? d) x-intercept(s) = (write in point form) e) y-intercept(s) = (write in point form) f) Two additional points other than the vertex or intercepts (one on each side of the vertex): %3D %3D %3| g) Graph (Draw & Label x and y axes):

Q: verify that w xy = w yx . w= (3x - y)/(x+y)

A: We find w_x first using partial derivative with respect to x and use the quotient rule.

Q: Graph each of the following over two periods. f(x) =-3 +2sin(2x) f(t)=4+ cos(8t) f(x)=(-(5/2))(cos3(...

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Q: please show all steps

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Q: Is there a direction u in which the rate of change of ƒ(x, y) = x2 - 3xy + 4y2 at P(1, 2) equals 14?...

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Q: What is the average rate of change of the function g(t) over the interval from t = a to t = b? How i...

A: The average rate of change of the function g(t) over the interval from t = a to t = b is given by: ...

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Graph the equation r = sin^2 (2.3u) + cos^4 (2.3u) for 0 <=u<= 10pai.

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Q: find the average rate of change of the function over the given interval or intervals. 1. g(x) = x2 -...

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Q: Find all the second-order partial derivatives of the functions 41. w = ye^(x2-y) 42.w= (x - y)/( x2 ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find the areas of the regions . 1.Inside the circle r = -2 cos u and outside the circle r = 1 2. Ins...

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Q: Assume that 1<a<b and a/x+ x = 1 /(x - b) . Show that this equation is solvable.

A: Given that the equation, To solve the equation,

Q: Find the Oimits :- sin 3y Lim Sin Jz8 Lim My JzO ot

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: use graphing software to determine which of the given viewing windows displays the most appropriate ...

A: We will graph ƒ(x) = x^4 - 7x^2 + 6x in all the given windows and then check which one works best.  ...

Q: Of (x-2)-3 Use the following graph of f(x) to sketch the requested graphs in parts a and b. B)f(-x)

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Q: The average temperature  in Dumboldt Valley is given by the following function T(x)=37 +10 sin((2pi/...

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Q: If  z = x2y + yex2, find zyx(3,6)  (Give an exact answer. Do not round.)

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Q: use the formal definition of limit to prove that the function has a continuous extension to the give...

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Q: Suppose that 2 < f '(x) < 5 for all values of x. What are the minimum and maximum possible values of...

A: The given inequality is 

Q: Prove the limit Constant Multiple Rule:  lim x--&gt;c kƒ(x) = k lim x--&gt;c ƒ(x) for any constant k...

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Q: Give an informal or intuitive definition of the limit ƒ(x) = L. as lim x--&gt;c Why is the definitio...

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Q: The temperature T = T(x, y) in °C at point (x, y) satisfies Tx(1, 2) = 3 and Ty(1, 2) = -1. If x = e...

A: We find x and y at t=1 And dx/dt and dy/dt at t=1  

Q: Find all the second-order partial derivatives of the functions 41.ƒ(x, y) = x2y3 - x4 + y5 42. z = x...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: A bug crawls on the surface z = x2 - y2 directly above a path in the xy-plane given by x = ƒ(t) and ...

A: We are given that the bug crawls on the surface z = x2 - y2 and x = ƒ(t) and y = g(t).  So,         ...

Q: For what values of b is b + 1' x? + b, x > 0 8(x) = continuous at every x?

A: Now we check the continuity at x = 0:

Q: As you may know, most metals expand when heated and contract when cooled. The dimensions of a piece ...

A: We are given  y = 10 + (t - 70) * 10^-4 centimeters. And we need to find t such that its width stay ...

Q: What is the value of lim u--&gt;0 ((sin u)/u)? Does it matter whether u is measured in degrees or ra...

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Q: Determine the domain and range of each function. Use various limits to find the asymptotes and the r...

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Q: Use limits to determine the equations for all vertical asymptote. y=(x2-x-2)/(x2-2x+1)

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Q: Find the slopes of the curves in Exercises 17–18 at the given points. Sketch the curves along with t...

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Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: if g(x) is an odd function defined for all values of x,what can you sat about g(0)

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Q: sketch the interval (a, b) on the x-axis with the point c inside. Then find a value of d &gt; 0 such...

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Q: find the integral of tan5x dx

A: We want to evaluate the following integral,

Q: The lengths a, b, and c of the edges of a rectangular box are changing with time. At the instant in ...

A: Volume= V=length*width*height  V=abc Find dV/dt using product rule and then plug the given values an...

Q: To estimate the ages of trees, forest rangers use a linear model that relates tree diameter, d (in i...

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Q: Suppose a triangle has vertices A, B and C and has the following measurements: m/C = 91° AC = 39.9 c...

A: Given,  

Q: Find all the second-order partial derivatives of the functions 41.w = x2 tan (xy) 42. w = x sin (x^2...

A: (Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new que...

Q: Use the graph to state the absolute and local maximum and minimum values of the function. (Assume ea...

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Q: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what h...

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Q: Use the following graph of f(x) to sketch the graph of f(x-2)-3.

A: The graph of f(x) is given.

Q: use the formal definition of limit to prove that the function is continuous at c.  ƒ(x) = x2 - 7, c ...

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Q: determine whether the series converges or diverges. If it is convergent, find the sum

A: We will apply the ratio test to figure out if the series is convergent or not. Let's take the ratio ...

Q: Show that the function F(x) = (x - a)2. (x - b)2 + x takes on the value (a + b)/2 for some value of ...

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Q: Once you know lim x--&gt;a+ f(x)  and lim x--&gt;a-  ƒ(x) at an interior point of the domain of ƒ, d...

A: If we know the right and left-hand limit of a point then we know the limit at that point.  

Q: Find its area (if the area is finite). (If the area is not finite, enter o.)

A: To determine the area of the bounded region.

Q: Find the areas of the regions . 1. Inside the lemniscate r^2 = 6 cos 2u and outside the circle r = s...

A: (Note:We’ll answer the first question since the exact one wasn’t specified. Please submit a new ques...

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the oute...

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Q: Use limits to determine the equations for all vertical asymptotes. y=(x2+4)/(x-3)

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Q: Find the average rate of change of f(x)= 3 * square root of x-1 on the interval [2, 10].

A: Given function and interval 

Q: Find f'(0), f''(0), and and determine whether f has a local minimum, local maximum, or neither at x ...

A: We find f'(x) using the power rule and the chain rule. Then plug x=0 in it.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.