Mathematics1 (ENG 021) - Past Paper - New Ismailia National University - Sheet 3 - PDF

‫ جامعة اإلسماعيلية الجديدة األهلية‬- ‫كليــــــــة الهندســـــــة‬ Faculty of Engineering – New Ismailia National University AIEP PROGRAM MATHEMATICS1 (ENG 021)...

‫ جامعة اإلسماعيلية الجديدة األهلية‬- ‫كليــــــــة الهندســـــــة‬ Faculty of Engineering – New Ismailia National University AIEP PROGRAM MATHEMATICS1 (ENG 021) Dr. Amr H. Abdalla Sheet (3) Choose the correct answer: 1) The graph of the function 𝑓(𝑥) = 𝑠𝑖𝑛(𝑠𝑖𝑛−1 (𝑥)) is A) B) C) D) 2) Find the domain of the following functions 𝑓(𝑥) = 3𝑠𝑖𝑛−1 (𝑥 − 1) A) 𝑅 B) (0, ∞) C) [0,2] D) None of these −1 3) The Range of the function ℎ(𝑥) = 3𝑠𝑖𝑛 (𝑥 + 1) 3𝜋 3𝜋 3𝜋 A) 𝑅 B) [0, 2 ] C) [− 2 , 2 ) D) None of these 7𝜋 4) 𝑐𝑜𝑠 −1 (𝑐𝑜𝑠 ( 4 )) = ⋯ 𝜋 7𝜋 A) 𝑧𝑒𝑟𝑜 B) 4 C) 4 D) None of these 5) The Range of 𝑓(𝑥) = 2 𝑡𝑎𝑛−1 (𝑥) 𝜋 𝜋 A) (−𝜋, 𝜋) B) (− 2 , 2 ) C)[0,2𝜋) D) None of these - Determine whether the following functions are even, odd, or neither even nor odd. 6) ℎ(𝑥) = √𝑠𝑖𝑛−1 (𝑥 2 ) 1 A) Even B) Odd C) Neither even nor odd 7) 𝑓(𝑥) = √𝑠𝑖𝑛−1 (𝑥 3 ) A) Even B) Odd C) Neither even nor odd −1 8) 𝑓(𝑥) = 𝑡𝑎𝑛 (√sin (𝑥 3 )) A) Even B) Odd C) Neither even nor odd 𝑐𝑜𝑠 −1 𝑥 9) 𝑔(𝑥) = 𝑡𝑎𝑛−1 ( 𝑠𝑖𝑛−1 𝑥 ) A) Even B) Odd C) Neither even nor odd −1 1 10) 𝑡𝑎𝑛 (𝑥) = ⋯ A) 𝑐𝑜𝑠 −1 (𝑥) B) 𝑐𝑜𝑡 −1 (𝑥) C) 𝑐𝑠𝑐 −1 (𝑥) D) None of these 1 11) 𝑠𝑒𝑐 −1 (𝑥) + 𝑠𝑖𝑛−1 (𝑥) = ⋯ 𝜋 A) zero B) 𝜋 C) 2 D) None of these 12) sin(𝑠𝑒𝑐 −1 (𝑥) + 𝑐𝑠𝑐 −1 (𝑥)) = ⋯ 𝜋 A) zero B) 𝜋 C) 2 D) None of these 13) The simplification of 𝑓(𝑥) = 𝑠𝑖𝑛 (𝑐𝑜𝑠 −1 (√1 − 𝑥)) is A) 𝑓(𝑥) = √1 − 𝑥 B) 𝑓(𝑥) = √1 − 𝑥 2 C) 𝑓(𝑥) = √𝑥 D) None of these 1+𝑡𝑎𝑛ℎ𝑥 14) The solution of the equation 𝐿𝑛 (1−𝑡𝑎𝑛ℎ𝑥) = 4 is A) {2} B) {1,4} C) {0,2} D) None of these 15) The set of solution of the equation 𝑐𝑜𝑠ℎ(𝐿𝑛𝑥) = 2 sinh(𝐿𝑛𝑥) − 1 is A) {3, −1} B) {3} C) {1,3} D) None of these 4𝑥 1 16) 𝑒 + 4𝑥 = ⋯ 𝑒 A) 𝑐𝑜𝑠ℎ4𝑥 B) 𝑠𝑖𝑛ℎ4𝑥 2𝑐𝑜𝑠ℎ4𝑥 D) 2𝑠𝑖𝑛ℎ4𝑥 17) 𝐿𝑛(𝑒 2𝑥 − 1) − 𝐿𝑛(2𝑒 𝑥 ) = ⋯ A) 𝐿𝑛(𝑠𝑖𝑛ℎ2𝑥) B) 𝐿𝑛(𝑠𝑖𝑛ℎ𝑥) C) 𝐿𝑛(𝑥) D) None of these 18) ) 𝑐𝑜𝑠ℎ 𝑥 + 𝑠𝑖𝑛ℎ 𝑥 = ⋯ A) 1 B) 𝑒 −𝑥 C) 𝑒 𝑥 D) None of these 19) The set of solution of the equation 24 sinh(𝑥) − 12𝑐𝑜𝑠ℎ(𝑥) − 3 = 0 is 3 A) {2, − 2} B) {𝐿𝑛(2), 0} C) {𝐿𝑛(2)} D) None of these 20) coth(𝐿𝑛(𝑥)) = ⋯ 𝑥 2 −1 𝑥 2 +1 𝑥 2 +1 A) 𝑥 2+1 B) 𝑥 2 −1 C) D) None of these 𝑥−1 2