α α₯αα½α α«ααα αααα΅α αααα΅ ααα½α αα α
α α αα½α ααα© α αα αα α ααα α΅ααα΅ αα α ααα³α α°α½αα ααα α α¨ααα #α€αα΅α΅αͺα_α α΅α ααα½α αααααα’ αααα΅α α α αα£α‘ α αα αα αα€α³ααα΅α α¨α α«α΅ααβοΈ
π³ #αα°αα₯απ
π° #α₯α«α΅α α αα’αα΅α αα¨αα©πΈπ΅
#α α΅α α_ααα_α¨ααα
αααααα₯ α @sademp #REGISTER α₯αα α«ααα©απ
#α€αα΅α΅αͺα_α α΅α ααα½
#ααα α_α¨α°α»α_αα_α¨αα«αααπ
π³ #αα°αα₯απ
π° #α₯α«α΅α α αα’αα΅α αα¨αα©πΈπ΅
#α α΅α α_ααα_α¨ααα
αααααα₯ α @sademp #REGISTER α₯αα α«ααα©απ
#α€αα΅α΅αͺα_α α΅α ααα½
#ααα α_α¨α°α»α_αα_α¨αα«αααπ
β€2π2π₯1π€1
π―α αα΅ 12α ααα α°αα³α α°ααͺ α¨αα΅ αα«αααΈα α¨ααα‘ α¨αα΅α΅ αααααα½!!!
1. Pythagorean theorem: aΒ² + bΒ² = cΒ²
2. Quadratic formula: x = (-b Β± β(bΒ² - 4ac)) / 2a
3. Distance formula: d = β((xβ - xβ)Β² + (yβ - yβ)Β²)
4. Slope-intercept form of a line: y = mx + b
5. Point-slope form of a line: y - yβ = m(x - xβ)
6. Midpoint formula: ((xβ + xβ)/2, (yβ + yβ)/2)
7. Law of sines: a/sin A = b/sin B = c/sin C
8. Law of cosines: cΒ² = aΒ² + bΒ² - 2ab cos C
9. Sum of angles in a triangle: A + B + C = 180Β°
10. Area of a triangle: A = (1/2)bh
11. Volume of a sphere: V = (4/3)ΟrΒ³
12. Volume of a cylinder: V = ΟrΒ²h
13. Volume of a cone: V = (1/3)ΟrΒ²h
14. Surface area of a sphere: A = 4ΟrΒ²
15. Surface area of a cylinder: A = 2ΟrΒ² + 2Οrh
16. Surface area of a cone: A = ΟrΒ² + Οrs, where s is the slant height
17. Binomial theorem: (a + b)βΏ = Ξ£(n choose k)a^(n-k)b^k, where Ξ£ is the sum from k=0 to n, and (n choose k) is the binomial coefficient
18. Fundamental theorem of calculus: β«a^b f(x) dx = F(b) - F(a), where F is the antiderivative of f
19. Derivative of a constant: d/dx(c) = 0
20. Power rule for derivatives: d/dx(xβΏ) = nx^(n-1)
21. Product rule for derivatives: d/dx(fg) = f'g + fg'
22. Quotient rule for derivatives: d/dx(f/g) = (f'g - fg')/gΒ²
23. Chain rule for derivatives: d/dx(f(g(x))) = f'(g(x))g'(x)
24. Mean value theorem: if f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = (f(b) - f(a))/(b-a)
25. Intermediate value theorem: if f is continuous on [a,b], then for any y between f(a) and f(b), there exists c in [a,b] such that f(c) = y
26. Rolle's theorem: if f is continuous on [a,b] and differentiable on (a,b), and if f(a) = f(b), then there exists c in (a,b) such that f'(c) = 0
27. Integration by substitution: β«f(g(x))g'(x) dx = β«f(u) du, where u = g(x)
28. Integration by parts: β«u dv = uv - β«v du
29. L'Hopital's rule: if lim(x β a) f(x)/g(x) = 0/0 or β/β, then lim(x β a) f(x)/g(x) = lim(x β a) f'(x)/g'(x)
30. Taylor series: f(x) = Ξ£(n=0 to β) f^(n)(a)/n!(x-a)^n, where f^(n) is the nth derivative of f
31. Euler's formula: e^(ix) = cos(x) + i sin(x)
32. De Moivre's theorem: (cos x + i sin x)^n = cos(nx) + i sin(nx)
33. Fundamental trigonometric identities: sinΒ² x + cosΒ² x = 1, 1 + tanΒ² x = secΒ² x, 1 + cotΒ² x = cscΒ² x
34. Double angle formulas: sin 2x = 2sin x cos x, cos 2x = cosΒ² x - sinΒ² x, tan 2x = (2tan x)/(1 - tanΒ² x)
35. Half angle formulas: sin(x/2) = Β±β((1 - cos x)/2), cos(x/2) = Β±β((1 + cos x)/2), tan(x/2) = Β±β((1 - cos x)/(1 + cos x))
36. Sum-to-product formulas: sin A + sin B = 2sin((A+B)/2)cos((A-B)/2), cos A + cos B = 2cos((A+B)/2)cos((A-B)/2), sin A - sin B = 2cos((A+B)/2)sin((A-B)/2), cos A - cos B = -2sin((A+B)/2)sin((A-B)/2)
37. Product-to-sum formulas: cos A cos B = (1/2)(cos(A-B) + cos(A+B)), sin A sin B = (1/2)(cos(A-B) - cos(A+B)), sin A cos B = (1/2)(sin(A+B) + sin(A-B)), cos A sin B = (1/2)(sin(A+B) - sin(A-B))
38. Hyperbolic functions: sinh x = (e^x - e^-x)/2, cosh x = (e^x + e^-x)/2, tanh x = sinh x/cosh x
39. Inverse trigonometric functions: arcsin x, arccos x, arctan x
40. Logarithmic identities: log(xy) = log x + log y, log(x/y) = log x - log y, log x^n = n log x
41. Exponential identities: e^x+y = e^x e^y, (e^x)^n = e^(nx), e^0 = 1
42. Binomial coefficients: (n choose k) = n!/(k!(n-k)!)
https://t.me/extremetutor
1. Pythagorean theorem: aΒ² + bΒ² = cΒ²
2. Quadratic formula: x = (-b Β± β(bΒ² - 4ac)) / 2a
3. Distance formula: d = β((xβ - xβ)Β² + (yβ - yβ)Β²)
4. Slope-intercept form of a line: y = mx + b
5. Point-slope form of a line: y - yβ = m(x - xβ)
6. Midpoint formula: ((xβ + xβ)/2, (yβ + yβ)/2)
7. Law of sines: a/sin A = b/sin B = c/sin C
8. Law of cosines: cΒ² = aΒ² + bΒ² - 2ab cos C
9. Sum of angles in a triangle: A + B + C = 180Β°
10. Area of a triangle: A = (1/2)bh
11. Volume of a sphere: V = (4/3)ΟrΒ³
12. Volume of a cylinder: V = ΟrΒ²h
13. Volume of a cone: V = (1/3)ΟrΒ²h
14. Surface area of a sphere: A = 4ΟrΒ²
15. Surface area of a cylinder: A = 2ΟrΒ² + 2Οrh
16. Surface area of a cone: A = ΟrΒ² + Οrs, where s is the slant height
17. Binomial theorem: (a + b)βΏ = Ξ£(n choose k)a^(n-k)b^k, where Ξ£ is the sum from k=0 to n, and (n choose k) is the binomial coefficient
18. Fundamental theorem of calculus: β«a^b f(x) dx = F(b) - F(a), where F is the antiderivative of f
19. Derivative of a constant: d/dx(c) = 0
20. Power rule for derivatives: d/dx(xβΏ) = nx^(n-1)
21. Product rule for derivatives: d/dx(fg) = f'g + fg'
22. Quotient rule for derivatives: d/dx(f/g) = (f'g - fg')/gΒ²
23. Chain rule for derivatives: d/dx(f(g(x))) = f'(g(x))g'(x)
24. Mean value theorem: if f is continuous on [a,b] and differentiable on (a,b), then there exists c in (a,b) such that f'(c) = (f(b) - f(a))/(b-a)
25. Intermediate value theorem: if f is continuous on [a,b], then for any y between f(a) and f(b), there exists c in [a,b] such that f(c) = y
26. Rolle's theorem: if f is continuous on [a,b] and differentiable on (a,b), and if f(a) = f(b), then there exists c in (a,b) such that f'(c) = 0
27. Integration by substitution: β«f(g(x))g'(x) dx = β«f(u) du, where u = g(x)
28. Integration by parts: β«u dv = uv - β«v du
29. L'Hopital's rule: if lim(x β a) f(x)/g(x) = 0/0 or β/β, then lim(x β a) f(x)/g(x) = lim(x β a) f'(x)/g'(x)
30. Taylor series: f(x) = Ξ£(n=0 to β) f^(n)(a)/n!(x-a)^n, where f^(n) is the nth derivative of f
31. Euler's formula: e^(ix) = cos(x) + i sin(x)
32. De Moivre's theorem: (cos x + i sin x)^n = cos(nx) + i sin(nx)
33. Fundamental trigonometric identities: sinΒ² x + cosΒ² x = 1, 1 + tanΒ² x = secΒ² x, 1 + cotΒ² x = cscΒ² x
34. Double angle formulas: sin 2x = 2sin x cos x, cos 2x = cosΒ² x - sinΒ² x, tan 2x = (2tan x)/(1 - tanΒ² x)
35. Half angle formulas: sin(x/2) = Β±β((1 - cos x)/2), cos(x/2) = Β±β((1 + cos x)/2), tan(x/2) = Β±β((1 - cos x)/(1 + cos x))
36. Sum-to-product formulas: sin A + sin B = 2sin((A+B)/2)cos((A-B)/2), cos A + cos B = 2cos((A+B)/2)cos((A-B)/2), sin A - sin B = 2cos((A+B)/2)sin((A-B)/2), cos A - cos B = -2sin((A+B)/2)sin((A-B)/2)
37. Product-to-sum formulas: cos A cos B = (1/2)(cos(A-B) + cos(A+B)), sin A sin B = (1/2)(cos(A-B) - cos(A+B)), sin A cos B = (1/2)(sin(A+B) + sin(A-B)), cos A sin B = (1/2)(sin(A+B) - sin(A-B))
38. Hyperbolic functions: sinh x = (e^x - e^-x)/2, cosh x = (e^x + e^-x)/2, tanh x = sinh x/cosh x
39. Inverse trigonometric functions: arcsin x, arccos x, arctan x
40. Logarithmic identities: log(xy) = log x + log y, log(x/y) = log x - log y, log x^n = n log x
41. Exponential identities: e^x+y = e^x e^y, (e^x)^n = e^(nx), e^0 = 1
42. Binomial coefficients: (n choose k) = n!/(k!(n-k)!)
https://t.me/extremetutor
Telegram
Extreme Consultancy and Training PLCβ’
Extreme Educational Consultancy and Training Center, the premier destination for comprehensive educational support and training services in Ethiopia.
π +251929835602
Megenagna, Genet Commercial No 09
https://extremeconsultancy.net/
π +251929835602
Megenagna, Genet Commercial No 09
https://extremeconsultancy.net/
π13β€5