limx→−∞x5tan(1πx2)+3|x|2+7|x|3+7|x|+8is equal to
−1/π
limx→−∞x5tan(1πx2)+3|x|2+7|x|3+7|x|+8limx→−∞x5tan(1πx2)+3x2+7−x3−7x+8 [∵ x<0⇒|x|=−x]On dividing the numerator and denominator by x3limx→−∞x2tan(1πx2)+3x+7x3−1−7x2+8x3limx→−∞1πtan{1πx2}+3x+7x31(πx2)−1−7x2+8x3
Since [x→−∞⇒1πx2→0 and limθ→0tanθθ=1]=1π.1+0+0−1−0+0=−1π