The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.
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Transcript of The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.
![Page 1: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/1.jpg)
The equation of the tangent to the curve 2x2 - y4 = 1 at the point
(1,1) is this.
What is y=x?
![Page 2: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/2.jpg)
What is infinity?
x 2
5lim
x 2
is this.
![Page 3: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/3.jpg)
is this.
What is + C
1dx
x ln x
21(ln x) C
2
![Page 4: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/4.jpg)
is also this function.
What is ?
2sin(2x) cos (2x)dx
31cos (2x) C
6
![Page 5: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/5.jpg)
If f(x) is continuous,f(1) = 8 and f(4) = -3, this theorem
tells me that f(x) must pass the x-axis at least once between
x=1 and x=4.
What is the Intermediate Value Theorem?
![Page 6: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/6.jpg)
The Mean Value Theorem tells us that if a function is differentiable on an interval then there is a value in
that interval at which the slope of the tangent line is equal to this quantity.
What is the average rate of change on the interval?
Or
What is the slope of the secant line?
![Page 7: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/7.jpg)
The derivative of y = ln(u) with respect to x is this.
1 du
u dxWhat is ?
![Page 8: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/8.jpg)
This graph can assist in visualizing the solution to a
differential equation.
What is a slope field?
![Page 9: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/9.jpg)
has a horizontal asymptote at this line.
What is y=0?
4 2
2 5
3x 2x x 1y
5 2x 3x
![Page 10: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/10.jpg)
These are values where the derivative of a function is zero or
undefined.
What are critical points?
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This ancient mathematical cult hid the existence of irrational
numbers fearing their impact on mathematics.
Who are the Pythagorians?
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This mathematician is most well known for the theorem stating that has no integer
solutions for a, b, and c when n is a natural number greater than 2.
Who is Fermat?
n n na b c
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This famous mathematician / computer scientist was submitted
to experiments using drugs because of his sexual preference.
Who is Alan Turing?
![Page 14: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/14.jpg)
This French mathematician died in a duel at the age of 20…
leaving behind a legacy of hastily scribbled theorems.
Who is Evariste Galois?
![Page 15: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/15.jpg)
This is the full name of the English mathematician who co-created the study of Calculus.
Who is Sir Isaac Newton?
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is this.
What is ?
a
dlog u
dx
1 du
(ln a)(u) dx
![Page 17: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/17.jpg)
The area between y = x2 and y=x is this number.
What is 1/6?
![Page 18: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/18.jpg)
gives this family of functions.
What is ?
2
3
3x 2dx
x 2x 6
3ln x 2x 6 C
![Page 19: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/19.jpg)
The slope of the tangent line to the curve given by
xy2 + 2xy + 3x = 4 when x = 2 is this.
What is undefined?
![Page 20: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/20.jpg)
The area between the graphs of cosx and sinx between two consecutive intersection points.
What is ?2 2
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sin2(4θ) + cos2(4θ) is always this number.
What is One?
![Page 22: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/22.jpg)
As long as b≠0, then if logba=0, a must be this
number.What is 1?
![Page 23: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/23.jpg)
The limit of (sin x)/x as x approaches zero.
What is one?
![Page 24: The equation of the tangent to the curve 2x 2 - y 4 = 1 at the point (1,1) is this.](https://reader038.fdocuments.us/reader038/viewer/2022110211/56813296550346895d992d02/html5/thumbnails/24.jpg)
The area between x=0 and x=π bounded by the
x-axis and the sine function.
What is 1 +1?
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Song by Bob Marley whose title might have
been a better name for this category.
What is “One Love”?
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DAILYDOUBLE
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DAILYDOUBLE
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FINALJEOPARDY
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CALCPARDY
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The formula for the surface area of a sphere
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If f(x) is continuous,f(1) = 8 and f(4) = -3, this theorem
tells me that f(x) must pass the x-axis at least once between
x=1 and x=4.
What is the Intermediate Value Theorem?