Canya's Calculating Captivating Catastrophic Classy Clinical (and Cunty) Calculus (ABAP) Criterion

Push Me to My Limitsssss 😩

100

The

lim              x²

x→0     _________

              1 - cos² x

What is 1?

200

The

lim         tanx

x→0     ______

              69x

What is 1/69?

300

The

lim         5^x - 3^-x

x→∞     ________

              5^x + 4^-x

What is 1?

400

The

lim       ln(x + h) - ln(x)

h→0    ______________

                     h

when x = 2e

What is 1/(2e)?

500

The value of a if

lim         arccsc(a + h) - arccsc(a)

h→0     _____________________ = 2

                             h

What is

a = ± √ (  1 + √(2))

          ___________    ?   

                  2)

The Best Type of Curves 😉

100

The average velocity of a particle over the first two seconds that moves from its initial position so that after t seconds, its distance is given by 

s(t) =        4

         __________

            3t + 2

 from its initial position.

What is -3/4^ft/sec ?

200

The body's accelaration each time the velocity is zero if the position of a body at a time t minutes is 

s(t) = t³ - 15t² +72t +10

What is ±6^{m/min squared}

300

The intervals the graph of f is concave up if the function f has first derivative given by 

f^'(x) = x⁴ - 6x² - 8x -3

What is (2, ∞)?

400

The largest open interval on which the graph of f is both concave up and increasing if 

f (x) = -3 + 6x² - 2x³

What is (0, 1) 

500

The values of a and b so that f(x) is differentiable at x=0

f(x) =  {x²+4x+1, x≥0

           {asin(3x) + bcos(2x), x<0

What is when a = 4/3 and when b =1?

X Marks the Spot 🤭

100

If f is the function given by 

f(x) = (4/x) +5x -1

then f^'(2)

What is 4?

200

f^'(x) if 

f(x) = x⁵ - 5^x

What is

5x⁴ - (ln 5)5^x ? 

300

The equation of the line tangent to the graph f(x) at the point (3 ln 4, 4) if  

f(x) = e^x/3

What is

y - 4 = (4/3)(x - 3 ln 4)?

400

The equation of the tangent line:

y = log₂ (3x - 4) at x=4

What is

y − 3 =      3        *   (x−4) ?

             _______

              8 ln(2)

500

(dy/dx) at the point (2,8) if 

x + 3y^1/3 = y

What is 4/3?

Stuff I Still Don't Know How to Solve 🤷🏾

100

The

lim             5^x

x→-∞     ______

                  2^x

What is 0?

200

The value of x at which the minimum value of 

y = 3x^4/3 - 2x 

occurs on the closed interval [0,1]

What is 1/8?

300

dR/dA for the following equation where w, y and V are constants.

R = 2w⁵√(A) - (4y³)

                      ------

                     (A²-6V)

What is

R = (2w)               (8y³A)

     _______   +     _______ ?

      (5√(A⁴)           (A²-6V)²

400

(dy/dx) at x=(π/3)

if y = sinxcosx 

What is -1/2

500

The relative minimum and maximum for the function

f(x) =        2

         _________

              x² - 4

What is -1/2?

....

(I think?)

Canya's Greatest Fumbles 😔

100

The

lim       2x² - x - 15 

x→3     _________

              x³ - 27

What is 11/27?

200

lim         sin(2(x + h) - sin(2x))

h -> 0   ___________________

                         h

for any real number x

What is 

2cos(2x)?

300

 x      f(x)       g(x)       f^'(x)      g^'(x)

-1        7           3          -3          -5

 3        2          -2           6           4

---------------------------------------------

The derivative of:

((g(x) + 2)/(x + f(x))

at x = -1

What is -5/9?

400

The value(s) of c on (a,b)  that satisfies the MVT if:

f(x) = ln(4x - 3), [1,5],

and f(x) is differentiable on [1,5]

What is    (16 + 3 ln 17)

              _____________ ?

                 (4 ln 17)

500

 (x)|     0|     4|     8|     12|     16|

----------------------------------------   

f(x)|     8|     0|     2|     10|     1  |

The following intervals in which there must be a number c such that f^'(c) = 2 if the table above gives selected values for the differentiable function f.

What is (8,12)?