Trigonometric Limits

JEE Main Mathematics · Limits · 7 questions, latest first

• Let f(x)= lim_y → 0 ((1- cos (x y)) tan (x y))/y^3. Then the number of solutions of the equation f(x)= sin x, x ∈ R is:20265 April, Shift 2 · Q17
• The value of lim_x → 0 (log_e( sec (e x) · sec (e^2 x) · … · sec (e^10 x)))/(e^2-e^2 cos x) is equal to202628 January, Shift 1 · Q18
• lim_x → 0^+ (tan (5(x)^(1/3)) log_e(1+3 x^2))/(( tan^-1 3 √x)^2(e^5(x)^(4/3)-1)) is equal to20257 April, Shift 1 · Q16
• The value of lim_x → 0 2((1- cos x √(cos 2 x) √[3](cos 3 x) … ….. √[10](cos 10 x))/x^2) is ____.20248 April, Shift 1 · Q26
• Let a>0 be a root of the equation 2 x^2+x-2=0. If lim_x → 1/a (16(1- cos (2+x-2 x^2)))/((1-a x)^2)=α+β √17, where α, β ∈ Z, then…20245 April, Shift 2 · Q23
• If α>β>0 are the roots of the equation a x^2+b x+1=0, and lim_x → 1/(α)((1- cos (x^2+b x+a))/(2(1-α…20238 April, Shift 2 · Q9
• lim_x → 0((((1- cos^2(3 x).)/(cos^3(4 x)))((sin^3(4 x))/(( log_e(2 x+1))^5))) is equal to ____20238 April, Shift 1 · Q10