Calculus Answers

find limit x approaches -2+ (x+3) [(|x+2|) / (x+2)]

limit as t →∞(4t^2-8)/(t-2)

for what value of k, is the function f, defined by,
f(x)={[sin(1+x)-sin(1-x)]/x, when x≠0 ; kcos1, when x=0
continuous at x=0?

find out for which value of k the function f, given by
f(x)={ (1-cos4x)/x^2 , when x≠0 ; k(2+sin^(2) x), when x=0
is continuous at x=0.

Vectors and have scalar product and their vector
product has magnitude . What is the angle between these two vectors?

Find the area bounded by a² y²= a² x² − x⁴

Determine the values of a and b for which the function
f(x)={ (sin3x+a sin2x +b sinx) / x^5 , x≠0 ; 1, x=0
is continuous at x=0

Evaluate ∫∫(x+2y)dA,
where D is the region bounded by the parabolas
y = 2x^2 and y =1+ x^2 .

If a and b represent the non-parallel segments of a parallelogram, express the diagonal vectors in terms of a and b

Find the area bounded by a^2x^2=a^2x^2-x^4.