calculator techniques 2

SESSION 3 PART 1 Differential Calculus

1. Find A. 0 B. 0.353 C. indeterminate D. infinity

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Code: I-type lang ang equation Press CALC.... . .x? Wag po natin i-substitute as x=0 dahil magmaMATH error po yan. Mag-isip po ng number na malapit sa 0. For example 0.001. Then press '=' .. And you will get the answer.

2. Find A. 0 B. 1.75 C. indeterminate D. infinity Code: Same method lang po sa #1. So, napaisip ka ngayon kung paano infinity?. Ano po ba ang infinity? Ito ay isang malaking number. So press CALC... .x? infinity = 1000 or kahit anong malaking number basta wag lang magMAMATH error. And you will get the answer.

3. Find A. -1 B. 1 C. -2 D. 2 Code:

Same method as #1.

4. Find A. 0 B. 1/3 C. 1 D. 3 Code: Same method lang din sa #1. Pero wag kalimutan na ilagay sa rad mode ang calcu.

5. Find A. 0 B. 1/3 C. 1 D. 3 Code: Same method as #4.

6. Find A. B. C. 0 D. infinity Code: Same method lang din as #4. Palitan ang x ng malapit sa 1. either 1.001 or .9999

7. Find the derivative of A. B. C.

D. Code: This time I assume na marunong na ang lahat at pamilyar na kayo sa mga steps at function na ginagawa natin. Don't forget: Always use rad mode in trigonometric and inverse trigonometric equations. Gamitin ang d/dx function. SHIFT>INTEGRAL then i-type ang equation. At maglagay ng value ng x. Youre favorite number. I preferred 5. Set x=5 Makakakuha tayo ng answer. Say A1(answer #1). Then mula sa choices, isubstitute lang ang 5 sa x at makakauha tayo ng sagot. Say A2 (answer #2) Kung A1 = A2 then tama ang napili niyo sa choices.

8. Find the derivative of y if A. B. C. D. Code: Same lang sa #7. I hope you get it. That's what you called reverse engineering.

9. Find the derivative of y if A. B. C. 1 + cos x D. 1 - cos x Code:

Same method with #7.

10. Find the derivative of y if tan y = x . A. B. sec x tan x C. D. Code: Ang technique lang lagi dito guys is that you must convert the equation into y into a function of x. That is,

Then yun, same method na lang as #7.

11. Find the first derivative of y if A. B. C. D. Same lang ito sa mga nakaraang examples ko sa differential calculus. Kung hindi niyo alam ito, basa muna kayo sa mga naunang example. NOTE: Pag parehas ang sagot, HUWAG GAMITIN ANG 1. USE 2 or 3.

12. Find the second derivative of y if A. B. C. D. So, mano-mano ito since walang shortcut pag second derivative. Sa board exam may ganyan. So let's test kung marunong pa kayo sa mano-mano.

13. Find the third derivative of y = x ln x. A. -1/x

B. -1/(x^2) C. -1/(x^3) D. -1 So, mano-mano ito since walang shortcut pag third derivative. Sa board exam may ganyan. So let's test kung marunong pa kayo sa mano-mano.

14. Find the derivative of y if A. -x/y B. x/y C. y^-3 D. -y^-3

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change to function of x then use d/dx function. Kayo na bahala kung anong value ng x gusto niyo. Then compare. Actually same lang ito sa #7.

15. Find the first derivative of y if A. y / (x+y) B. -y / (x+y) C. y / (x+2y) D. -y / (x+2y) Same lang sa #14.

16. Find the partial derivatives with respect to x of the function A. y^2 - 5 B. y^2 C. xy-5y D. 2xy Mag-iisip ka ng value ng y and then kapag dinirivative mo, equal siya dun sa value ng y. For example, y = 4. Substitute 4 in the equation. The equation now becomes 16x-20+6 or 16x-14. Then use (d/dx)(16x-4). Ang x natin dito ay always 1. So kung anong nakuha niyo answer diyan, kailangan mag equal siya dun sa answer. For example ang answer ay 16. Letter B and tamang sagot kasi y = 4 and y^2 = 16.

17. The function A. -1, 3 B. 1,-3 C. -1,2

is discontinous at

D. 1,-2 Use d/dx function then x=x and press CALC. Isubstitute ang lahat ng choices at kung saan nagerror, yun na.

18. Find the slope of the tangent line to the graph of the function at the point where x=3. A. 60 B. 66 C. 72 D. 78 Radian mode. Use d/dx function with x=3 Slope tangent is equal to the first derivative(y')

19. If y=4cos x + sin 2x, what is the slope of the curve when x = 2 radians? A. -2.21 B. -4.94 C. -3.21 D. 2.21 same with #18.

20. Find C so that the line y = 4x + 3 is tangent to the curve y = x^2 + C. A. 4 B. 5 C. 6 D. 7 Remember: m1=m2 (tangent/parallel) m1= -1/m2 (normal/perpendicular) And y=4x+3 should be tangent to y=x^2+C First, get the first derivative or slope of y=4x+3. Use d/dx with x=1, therefore the slope is 4. equate y' = y' (y=4x+3) = (y=x^2+C) 4 = 2x and x = 2. Then get the value of y from y=4x+3 y = 11. Therefore, our pt is (2,11) Substitute this to Y = x^2 + C to get the value of C.