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Solved in 2 steps with 2 images
- What is the purpose of the Intermediate Value Theorem?use the definition of the derivative to compute the derivative of the function f(x)=1−2x2 at an arbitrary point x. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). f′(x)=limh→0(f(x+h)−f(x)h)=limh→0( )= .Use the definition of the derviative to compute the derivative of f(x)=1−3x2f(x)=1−3x2 at the specific point x=2x=2. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box).
- Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.Let f(x)=1/x Using the definition of derivative at point f’(a)=lim f(x)-f(a)/x-a f’(3)=lim x->3___ After evaluating the limit we see that f’(3)=____ Finally the equation of the tangent line to f(x) where x=3 is ___Find the derivative of f(x) = √x^2 + 1 at a = 2, using the limit definition (i.e. first principles)
- Let f(x)=4x 2+12x−2Using the definition of derivative, f'(x)=limh→0 f(x+h)−f(x) /h,enter the expression needed to find the derivative at x=3.f'(x)=limh→0 After evaluating this limit, we see that f'(x)= Finally, the equation of the tangent line to f(x), in point-slope form, where x=3 is ------Find the derivative of f(x) = 1/√(x + 1) at x = 0 using the definition of the derivative as a limit. Be sure to justify your computations. Specifically, if at any point you evaluate a limit by inserting a value, explain WHY it is possible to do that.find the derivative of f(x)=x/(x+2) using the limit definition of a derivative
- (a)Find the equation of the tangent line to the curve f(x)=6x^2-5x+3 at the point where x=2. (Use the Basic Differentation Rules to find f'(x). That is, do not use the limit definition (b)Find the equation of the tangent line to thefunction: f(x) = 2x-1/x+2 when x=3lim as x-->0 of (x+1-cosx)/xFind lim by evaluating an appropriate definite integral over the interval [0, 1].