Concept - How to find limits with factorization method

Описание: Class XI_Limits

Concept – How to find limits with factorization method


Previous recorded questions and their links:
Q: Evaluate: ((a+h)^2⋅sin⁡(a+h)-a^2⋅sin⁡a)/h:    • Evaluate: ((a+h)^2⋅sin⁡(a+h)-a^2⋅sin⁡a)/h  
Q: Find the derivative of f(x)=ax+b, where a & b are non – zero constants, by first principle.:    • Find the derivative of f(x)=ax+b, where a ...  
Q: Find the derivative of f(x)=ax^2+bx+c, where a,b & c are non – zero constants, by first principle.:    • Find the derivative of f(x)=ax^2+bx+c, whe...  
Q: Find the derivative of 1/x by first principle.:    • Find the derivative of 1/x by first princi...  
Q: Find the derivative of f(x)=x^n, where n is a positive integer, by first principle.:    • Find the derivative of f(x)=x^n, where n i...  
Q: Find the derivative of f(x)=tan⁡(ax+b), by first principle.:    • Find the derivative of f(x)=tan⁡(ax+b), by...  
Q: Find the derivative of f(x)=e^√(tan⁡〖x^3 〗 ), by first principle.:    • Find the derivative of f(x)=e^√(tan⁡〖x^3 〗...  
Q: Evaluate: (lim)┬(x→2)⁡[1/(x-2)-2(2x-3)/(x^3-3x^2+2x)]:    • Evaluate: (lim)┬(x→2)⁡[1/(x-2)-2(2x-3)/(x^...  
Q: Evaluate: (lim)┬(x→0)⁡[(√(2+x)-√2)/x]:    • Evaluate: (lim)┬(x→0)⁡[(√(2+x)-√2)/x]  
Q: Find the positive integer n so that (lim)┬(x→3)⁡[(x^n-3^n)/(x-3)]=108:    • Find the positive integer n so that (lim)┬...  
Q: Evaluate (lim)┬(x→π/2)⁡(sec⁡x-tan⁡x ):    • Evaluate (lim)┬(x→π/2)⁡(sec⁡x-tan⁡x )  
Q: Evaluate (lim)┬(x→0)⁡〖(sin⁡(2+x)-sin⁡(2-x))/x〗:    • Evaluate (lim)┬(x→0)⁡〖(sin⁡(2+x)-sin⁡(2-x)...  
Q: Evaluate (lim)┬(x→π/6)⁡〖(2 〖sin〗^2⁡x+sin⁡x-1)/(2 〖sin〗^2⁡x-3 sin⁡x+1)〗:    • Evaluate (lim)┬(x→π/6)⁡〖(2 〖sin〗^2⁡x+sin⁡x...  
Q: Evaluate (lim)┬(x→0)⁡〖(tan⁡x-sin⁡x)/〖sin〗^3⁡x 〗:    • Q: Evaluate (lim)┬(x→0)⁡〖(tan⁡x-sin⁡x)/〖si...  
Q: Evaluate (lim)┬(x→a)⁡〖(√(a+2x)-√3 x)/(√(3a+x)-2√x)〗:    • Evaluate (lim)┬(x→a)⁡〖(√(a+2x)-√3 x)/(√(3a...  
Q: Evaluate (lim)┬(x→0)⁡〖(cos⁡ax-cos⁡bx)/(cos⁡cx-1)〗:    • Evaluate (lim)┬(x→0)⁡〖(cos⁡ax-cos⁡bx)/(cos...  
Q: Evaluate (lim)┬(n→∞)⁡〖((n+2)!+(n+1)!)/((n+2)!-(n+1)!)〗:    • Evaluate (lim)┬(n→∞)⁡〖((n+2)!+(n+1)!)/((n+...  
Q: Evaluate: (lim)┬(x→∞)⁡〖(2x-1)(3x+4)/(7x+2)(x+9) 〗 & (lim)┬(x→∞)⁡〖(√(2x^2-1)-√(5x^2+7))/(4x+1)〗:    • Evaluate: (lim)┬(x→∞)⁡〖(2x-1)(3x+4)/(7x+2)...  
Q: Evaluate: (lim)┬(x→∞)⁡〖((2x^2+3x+1)/(3x^2+4))^((4x+1)/(3x-7)) 〗:    • Evaluate: (lim)┬(x→∞)⁡〖((2x^2+3x+1)/(3x^2+...  
Q: Evaluate: (lim)┬(x→∞)⁡〖((x^2+1)/(7x^2-5x+3))^(4x+9) 〗:    • Evaluate: (lim)┬(x→∞)⁡〖((x^2+1)/(7x^2-5x+3...  
Q: Evaluate: (lim)┬(x→∞)⁡〖(2√x+3√(3&x)+4√(4&x)+⋯+n√(n&x))/((2x-3)^(1/2)+(2x-3)^(1/3)+(2x-3)^(1/4)+⋯+(2x-3)^(1/n) )〗:    • Evaluate: (lim)┬(x→∞)⁡〖(2√x+3√(3&x)+4√(4&x...  
Q: Evaluate (lim)┬(x→a)⁡〖(√(x^2+1)-√(3&x^2+1))/(√(5&x^5+1)-√(5&x^4+1))〗:    • Evaluate (lim)┬(x→a)⁡〖(√(x^2+1)-√(3&x^2+1)...  
Q: Evaluate (lim)┬(n→∞)⁡〖(1^100+2^100+3^100+⋯n^100)/n^102 〗:    • Evaluate (lim)┬(n→∞)⁡〖(1^100+2^100+3^100+⋯...  
Q: Evaluate (lim)┬(n→∞)⁡〖(1^3+2^3+3^3+⋯n^3)/n^4 〗-(lim)┬(n→∞)⁡〖(1^3+2^3+3^3+⋯n^3)/n^5 〗:    • Evaluate (lim)┬(n→∞)⁡〖(1^3+2^3+3^3+⋯n^3)/n...  
NCERT MISCELLANEOUS EXERCISE | Q14 – Q30:    • NCERT MISCELLANEOUS EXERCISE | Q14 – Q30  
Q: Solve (lim)┬(x→0)⁡〖(√(3&1+x^3 )-√(4&1-2x))/(x+x^2 )〗:    • Solve (lim)┬(x→0)⁡〖(√(3&1+x^3 )-√(4&1-2x))...  
Q: Solve (lim)┬(x→1)⁡〖(√(3&7+x^3 )-√(3+x^2 ))/(x-1)〗:    • Solve (lim)┬(x→1)⁡〖(√(3&7+x^3 )-√(3+x^2 ))...  
Q: Solve (lim)┬(x→0)⁡〖((4+x)^3-64)/x〗:    • Solve (lim)┬(x→0)⁡〖((4+x)^3-64)/x〗  
IMPORTANT RESULT FOR LIMITS & DERIVATIVES:    • IMPORTANT RESULT FOR LIMITS & DERIVATIVES  

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