Hello. Please provide explanation for the following questions. thanks!

f(-10 + h) - f(-10) Find the limit lim if f() = 943 - 6x2. h-+0 h f(-10 + h) - f(-10) lim hFind a and in so that the function is both continuous and differentiable. No two The tangent line to *5; Hz} at {2, 5} passes through the point {1, 2}. Compute the following. a.) HE} = [1.] fr} Let f and g be functions such that f(7) = 34, f'(7) = 3. f(34) = 12. f'(34) = -8. g(34) = -29, g'(34) = -10, g(12) = -27,and g'(12) = 52. (a) (g = f)'(34) = (b) (fo f)' (7) =Use linear approximation to approximate v 81.4 as follows. Let f(@) = v@. The equation of the tangent line to f() at = 81 can be written in the form y = ma + b. Compute m and b. Using this find the approximation for v81.4. Answer:The acceleration due to gravity, g, is given by GM 9 = where M is the mass of the Earth, r is the distance from the center of the Earth, and G is the uniform gravitational constant. (a) Suppose that we increase from our distance from the center of the Earth by a distance Ar = @. Use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: Ag = gx "Your answer will be a function of a and r.) (b) Is this change positive or negative? Ag is ? (Think about what this tells you about the acceleration due to gravity.) (c) What is the percentage change in g when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.29 km; assume the radius of the Earth is 6400 km)? percent change =