102-Unit 3_SG-HW - ENGR 102-Spring Unit 3 Study Guide Unit...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ENGR 102 -Spring Unit 3 Study Guide Unit Content: Section 6.7 7.1 7.7 Pages 456-464 466-475 517-534 Content Hydrostatic Pressures and Forces Inverse Functions and Their Derivatives Inverse Trigonometric Functions, Derivatives, and Integrals Involving Inverse Trigonometric Functions Learning Objectives: 1. Find the hydrostatic force on one side of a vertically-submerged plate with a given shape and of depth or the hydrostatic force on the inside of a given container (the weight density, the fluid is specified). Find of a given one-to-one function . Sketch a given and its inverse function on the same graph. Show that = = for a given one-to-one . Verify | = for a given and . Given the angle in terms of an inverse trigonometric function, sketch and label the corresponding triangle and find sin , cos , tan , cot , sec , and/or csc . Given a trigonometric function and an inverse trigonometric function or , or for a given .[Note: = only when falls in the evaluate range of principle values of .] Prove given inverse trigonometric identities. Prove geometrically + =. 2. 3. 4. 5. 6. 7. 8. 9. 10. Derive the formula for where is a given inverse trigonometric function. 11. State the integral formulas resulting from the derivatives of inverse trigonometric functions. 12. Evaluate or where involves an inverse trigonometric function and involves the derivative of an inverse trigonometric function. Unit 3 Homework Problems Homework 3 # Page 1 459 2 Problem 10 Notes/Hint/Answer Answer: 18w = 1161 lbf (#2-5) Find the hydrostatic force on one side of the vertically-submerged portion of the plate shown Answer: 128 3 15 Answer: 45 4 2 Answer: 86 5 3 Answer: 6 7 8 9 10 11 12 13 Use the centroid method to solve #3 above 460 473 473 474 474 474 474 13 2 5 17 18 21 22 Use the centroid method to solve (no credit for other methods). Homework 3 continued # Page Problem 14 Given (a) Find (b) Plot = = + 7, = −1 = and on the same graph. to show > 2, Find the value of at Notes/Hint/Answer . (c) Evaluate 15 16 = 530 = =0= 5 without finding . − 4 − 5, 3(a),(b),(c) (#17-23) Sketch and label reference triangles (sides and angle ) as shown in supplemental material (in DyKnow) and evaluate. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 cos cot sin −3 2 −2 3 = 3 5 , 2 < < ; cos =? ; tan =? cos = 1 3 , − 2 < < 0; sin =? ; tan =? tan = 1 2 , < < 3 2 ; sin =? ; cos =? Evaluate sec 2. Evaluate sin Evaluate sec 4. 3+ →∞ →∞ → Find the limit lim 1. . . . Find the limit lim Find the limit lim 532 531 531 531 531 532 532 532 532 532 532 534 549 1− 125 50 52 67 72 74 79 81 89 107 122 147 119 Answer: Answer: 2 + 3 + Answer: Answer: || Answer: = tan − +1 Note: tan = sec ...
View Full Document

Ask a homework question - tutors are online