Quiz Facts 6/ Mathematics - Calculus

Find the value for the function.Find f(x + h) when f(x) = -2x2 + 2x - 2.

Use l'Hopital's Rule to evaluate the limit.<img src="https://sciemce.com/files/4/ppg__ttttt0610191128__f1q115g1.jpg" style="vertical-align: -21.0px;" /><img src="https://sciemce.com/files/4/ppg__ttttt0610191128__f1q115g2.jpg" style="vertical-align: -17.0px;" />

3

Use the given triangles to evaluate the expression. Rationalize all denominators. <img src="https://sciemce.com/files/4/ppg__sas0525192030__f1q255g1.jpg" alt="" style="vertical-align: 0.0px;" height="204" width="332" />sin <img src="https://sciemce.com/files/4/ppg__sas0525192030__f1q255g2.jpg" style="vertical-align: -17.0px;" />

4

Write as the sum and/or difference of logarithms. Express powers as factors. log7<img src="https://sciemce.com/files/4/ppg__tttt0527191036__f1q179g1.jpg" style="vertical-align: -21.0px;" />

5

Find a formula for the nth partial sum of the series and use it to find the series' sum if the series converges.<img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q313g1.jpg" style="vertical-align: -21.0px;" /> + <img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q313g2.jpg" style="vertical-align: -21.0px;" /> + <img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q313g3.jpg" style="vertical-align: -21.0px;" /> + ... + <img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q313g4.jpg" style="vertical-align: -21.0px;" /> + ...

6

Solve the following system of equations by graphing. Round your answers to two decimal places, if necessary. <img src="https://sciemce.com/files/3/ppg__cognero__Section_3.5_Systems_of_Equations__media__f379df07-53a5-4c7a-8fb7-31027cf055a1.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_fc28bda9611041afae0fbdd41" />

7

Solve the problem.Find the center of mass of the region of constant density bounded from above by the sphere <img src="https://sciemce.com/files/4/ppg__10615191636__f1q92g1.jpg" alt="" style="vertical-align: -4.0px;" /> and from below by the cone <img src="https://sciemce.com/files/4/ppg__10615191636__f1q92g2.jpg" alt="" style="vertical-align: -4.0px;" />

8

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."sin 12π

9

Find the length of the curve.The spiral r = 4θ2, 0 ≤ θ ≤ 2<img src="https://sciemce.com/files/4/ppg__3rer0609191813__f1q24g1.jpg" style="vertical-align: -4.0px;" />

10

Decide which of the two given functions is linear and find its equation.

11

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (cos 3t)i + (2 sin t)j

12

Choose the equation that matches the graph.<img src="https://sciemce.com/files/4/ppg__as0610191727__f1q83g1.jpg" alt="" style="vertical-align: 0.0px;" height="200" width="200" />

13

Find the vertex of the parabola.y = x2 - 12x + 36

14

Express the sum in sigma notation.1 - 2 + 4 - 8 + 16

15

Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.<img src="https://sciemce.com/files/4/ppg__tttt0527191528__f1q57g1.jpg" alt="" style="vertical-align: -4.0px;" />n = 67n

16

Calculate dy/dt using the given information.<img src="https://sciemce.com/files/4/ppg__tttt0530191550__f1q67g1.jpg" style="vertical-align: -17.0px;" /> = x2 + y2; dx/dt = 12, x = 1, y = 0

17

Determine whether or not the graph is a graph of a function of x.<img src="https://sciemce.com/files/4/ppg__10612191829__f1q1g1.jpg" alt="" style="vertical-align: 0.0px;" height="201" width="200" />

18

Select the graph of the equation of the parabola. <img src="https://sciemce.com/files/2/ppg__cognero__Section_4.4_Translations_of_Conics__media__f7519459-f672-44af-8fd6-e3d49281d1a2.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_ddb5587a48544714bebdc826b" />

19

Find the length s. Round the answer to three decimal places.<img src="https://sciemce.com/files/4/ppg__rfde0526191616__f1q110g1.jpg" alt="" style="vertical-align: -4.0px;" />

20

Find the quotient and the remainder.-10x3 - 17x2 + 22x + 15 divided by 2x + 5

21

Solve the problem.For some inexact differential forms df, a function g(x, y, z) can be found such that dh = g(x, y, z) df is exact. When it exists, the function g(x,y,z) is called an "integrating factor". Show that g(x, y, z) = <img src="https://sciemce.com/files/4/ppg__10611192155__f1q194g1.jpg" style="vertical-align: -17.0px;" /> is an integrating factor for the inexact differential df = - <img src="https://sciemce.com/files/4/ppg__10611192155__f1q194g2.jpg" style="vertical-align: -17.0px;" /> dx + <img src="https://sciemce.com/files/4/ppg__10611192155__f1q194g3.jpg" style="vertical-align: -17.0px;" /> dy + <img src="https://sciemce.com/files/4/ppg__10611192155__f1q194g4.jpg" style="vertical-align: -17.0px;" /> dz.

22

Determine the exact values of the three trigonometric functions sine, cosine, and tangent of the angle θ. <img src="https://sciemce.com/files/2/ppg__cognero__Section_6.3_Trigonometric_Functions_of_Any_Angle__media__66a23169-73d1-462b-89ea-a0d985fdc90a.GIF" class="cognerograph" variablename="impvar_0fde68ddb9d14e33885e428ad" varid="variable_id_field" /> where <img src="https://sciemce.com/files/2/ppg__cognero__Section_6.3_Trigonometric_Functions_of_Any_Angle__media__6fe4912d-69ee-40c8-8c56-8c7f373cf214.PNG" class="wirisformula" align="middle" style="vertical-align: middle;" data-wiris-created="true" varid="variable_id_field" variablename="impvar_6f45b7c57b6b4b43aa7eaaeb9" />

23

Find the average value of <img src="https://sciemce.com/files/4/ppg__10612191744__f1q147g1.jpg" alt="" style="vertical-align: -4.0px;" /> over the given region.<img src="https://sciemce.com/files/4/ppg__10612191744__f1q147g2.jpg" alt="" style="vertical-align: -4.0px;" /> over the cube in the first octant bounded by the coordinate planes and the planes <img src="https://sciemce.com/files/4/ppg__10612191744__f1q147g3.jpg" alt="" style="vertical-align: -4.0px;" />, <img src="https://sciemce.com/files/4/ppg__10612191744__f1q147g4.jpg" alt="" style="vertical-align: -4.0px;" />, <img src="https://sciemce.com/files/4/ppg__10612191744__f1q147g5.jpg" alt="" style="vertical-align: -4.0px;" />

24

Find equilibrium points x, 0 ≤ x ≤ 1, for the following function.f(x) = <img src="https://sciemce.com/files/4/ppg__tttt0530191128__f1q20g1.jpg" style="vertical-align: -17.0px;" />x(1 - x2)

25

Calculate the arc length of the indicated portion of the curve r(t).r(t) = <img src="https://sciemce.com/files/4/ppg__ttt0613191016__f1q77g1.jpg" style="vertical-align: -17.0px;" /><img src="https://sciemce.com/files/4/ppg__ttt0613191016__f1q77g2.jpg" style="vertical-align: -4.0px;" />t3/2i + (5t sin t)j + (5t cos t)k ; -4 ≤ t ≤ 6

26

For what values of x does the series converge absolutely?<img src="https://sciemce.com/files/4/ppg__ewadas0609191750__f1q194g1.jpg" style="vertical-align: -23.0px;" />

27

Use L'H<img src="https://sciemce.com/files/4/ppg__tttt0610190958__f1q114g1.jpg" style="vertical-align: -4.0px;" />pital's rule to find the limit.<img src="https://sciemce.com/files/4/ppg__tttt0610190958__f1q114g2.jpg" style="vertical-align: -42.0px;" /><img src="https://sciemce.com/files/4/ppg__tttt0610190958__f1q114g3.jpg" style="vertical-align: -38.0px;" />

28

Find the quadratic approximation of f at x = 0.f(x) = ln(cos 8x)

29

Solve the problem.Using the following properties of a twice-differentiable function y = f(x), select a possible graph of f.<img src="https://sciemce.com/files/4/ppg__tttt0612191139__f1q16g1.jpg" style="vertical-align: -66.0px;" />

30

Determine the value of each variable.<img src="https://sciemce.com/files/4/ppg__sas0522191721__f1q157g1.jpg" style="vertical-align: -15.0px;" /> = <img src="https://sciemce.com/files/4/ppg__sas0522191721__f1q157g2.jpg" style="vertical-align: -15.0px;" />

31

Solve the inequality.x2 + 7x ≥ -12

32

Find the exact value of csc θ, using the triangle shown in the figure below, if a = 3 and b = 4. <img alt="" src="https://sciemce.com/files/2/ppg__cognero__Section_6.2_Right_Triangle_Trigonometry__media__28ddbec3-b1d0-46f4-825f-89b5f0349f6e.PNG" style="vertical-align:-115px;" width="204px" height="139px" />

33

Provide an appropriate response.Suppose a1, a2, a3, a4, a5, ... and b1= a1, b2= a3, <img src="https://sciemce.com/files/4/ppg__rtydfy0528191816__f1q329g1.jpg" alt="" style="vertical-align: -11.0px;" /> are sequences. Find the equation relating an and bn.

34

Divide numerator and denominator by the highest power of x in the denominator to find the limit.<img src="https://sciemce.com/files/4/ppg__tttt0612191002__f1q111g1.jpg" style="vertical-align: -21.0px;" /> <img src="https://sciemce.com/files/4/ppg__tttt0612191002__f1q111g2.jpg" style="vertical-align: -17.0px;" />

35

Find Dxy.y = 10 sinh-1 (ln x)

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Quiz Facts 6/ Mathematics - Calculus

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