Express the limit as a definite integral. [Hint: Consider f(x) = x*.] lim n- 00 dx

Q: Evaluate the definite integral by the limit definition

A: Here,

Q: (12|+ 3, if xs-3 Let f(x) ={ -2r, if -3 <x < 3 6r +2, if x2 3. Show that f(x) is continuous at x =…

A:

Q: (6x+3y)sin(2x+ y) lim (x,y)→(0,0) 4x² +4.xy+ y

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: (x² + 7x – 5, x 3' ih(x) on the interval [2,4].

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Is the function below, continuous as x tends to 5? f(x) = (2x - 6 (x² – 3x 2 - x < 5 x ≥ 5

A: We can solve this as follows:

Q: Evaluate f (x): at x = -2. %D 1 - x2 Select one: A. Discontinuous B. Continuous

A:

Q: Express the limit as a definite integral on the given interval. [3(x)³ - 7x*]4x, 2 lim i = 1 dx…

A:

Q: Use the limit definition to find the derivative of f (x), this means no short cut rules, f(x) = x? –…

A:

Q: The limit below represents a derivative f'(a). Find f(x) and a. (6+h)² - 36 h f(x) = a lim h→0

A:

Q: find lim x-> 0, cos (12x)-1 / 3x

A: Given,              limx→0cos 12x - 13x Move the term 1/3 outside of the limit because it is…

Q: Evaluate Hint: Use differentiation to show that n=1 (1 – x)-2 = nx"-! (for |x| < 1)

A: We have to show that 1-x-2=∑n=1∞nxn-1