If `f(x)=(x^(2)-3x+2)/(x^(2)-7x+12),` then which of the following limits exists? `(i)lim_(xtooo) sin^(-1)f(x)" "(ii)lim_(xtooo) cos^(-1)f(x)`
Text Solution
Verified by Experts
`underset(xtooo)lim(x^(2)-3x+2)/(x^(2)-7x+12)` `underset(xtooo)lim(1-(3)/(x)+(2)/(x^(2)))/(1-(7)/(x)+(12)/(x^(2)))` `=underset(xtooo)lim(1-(3)/(x))/(1-(7)/(x))" "`(Ignoring division with higher power) `=1^(+)" "("as "3//xlt7//x,"when "xlt0)` So, `underset(xtooo)limcos^(-1)f(x)`does not exist as `cos^(-1)x` is defined for `xin[1-,1].` Also`" "underset(xtooo)lim(1-(3)/(x)+(2)/(x^(2)))/(1-(7)/(x)+(12)/(x^(2)))=underset(xtooo)lim(1-(3)/(x))/(1-(7
)/(x))` `=1-" "("as "3//xlt7//x,"when "xlt0)` So, `underset(xtooo)limsin-1f(x)` exists.
LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS
CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos
Similar Questions
Explore conceptually related problems
Find the following limits: (i)lim_(xto0) (1)/(x)sin^(-1)((2x)/(1+x^(2)))" "(ii)lim_(xto0) (1)/(x)sin^(-1)(3x-4x^(3))
Among (i) lim_(xtooo) sec^(-1)((x)/(sinx))" and "(ii) lim_(xtooo) sec^(-1)((sinx)/(x)).
Find the limits of the following: (i)lim_(xto0) (sin3x)/(x)" "(ii)lim_(xto0) (sin7x)/(sin4x)" "(iii)lim_(xto0) (1-cos^(2)x)/(x^(2))
Evaluate lim_(xtooo) (sinx)/(x).
If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be correct (a) ("lim")_(x-> 1)f(x) for a=-2 (b) ("lim")(x->-2)f(x) for a=13 (c) ("lim")(x-> 1)f(x)=4/3 (d) ("lim")(x->-2)f(x)=-1/3
Evaluate lim_(xtooo)(1+2/x)^(x)
Evaluate: ("lim")_(xtooo)x^(1/x)
Evaluate the following limits : lim_(x rarr 0) (sin3x+7x)/(4x+sin2x)
