Find the limit algebraically.limh→0(f(5+h)−f(5)h) where f(x)=10x2−10x−2

limh→0(f(−2+h)−f(−2)h) where f(x)=−3x2−4x−9

Find the limit algebraically.limh→0(f(7+h)−f(7)h) where f(x)=−8x2+7x−9

limx→−3(3x2−6x+10)

. Find the value of α such that limx→−1 2x2−αx−14x2−2x−3 exists. Find the limit.2. Let limx→0 f (x)x2 = 5. Show that limx→0 f (x)x = 0.3. Let f : R → R and x0 ∈ R. Suppose limx→x0 f (x) exists. Show that limx→0 f (x + x0) =limx→x0 f (x).4. Let f (x) = |x| for every x ∈ R. Show that f is continuous on R.5. Let f : [0, π] → R be defined by f (0) = 0 and f (x) = xsin 1x − 1x cos 1x for x̸ = 0. Is fcontinuous ?6. Let f, g : R → R be continuous such that given any two points x1 < x2, there exists apoint x3 such that x1 < x3 < x2 and f (x3) = g(x3). Show that f (x) = g(x) for all x.

Find the limit (if it exists). (If an answer does not exist, enter DNE.)lim x→10 x + 6 − 4x − 10