5. Check the continuity as x approaches 3 and -3? X-3| f(x)= X- 3 6. sinx +cos, x#0 Show that the finction f(x)= is continuous at x = 0 X 2, x=0

Q: Ql) check the continuity of fX) at X=-1, 0,1.23 -1<x<1 x-4 2x-1, 3x-2 2, x=3 f(x) = 1sxs2 25x53 Q2)…

A: 1)

Q: Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following…

A: Given the functions, (a) fx=x+1 at a without numerical value. (b) fx=sinx+3 at a=0. (c) fx=xx+1 at…

Q: Let f(x) be a continuous function on (-00,0) and f"(x) = (-4x + 5)e4x. The function f(x) has an…

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Q: Q2/ A) Use the definition of the derivative to find f(x) where f(x)=v3x+1

A: To find the derivative of given f(x) using the definition of the derivative.

Q: (4) Find the derivative of f(x)= tanx+5

A:

Q: Q5: State and prove the theorem of (continuity-differentiability), then find the value(s) of x that…

A: As per the policy, we are solving first question. Please repost the question and specify which…

Q: Show that f is continuous on (∞ , -∞ )

A: Given Data The first function is f(x)= sin x. The second function is f(x)= cos x.   The limit of the…

Q: x2-8x+15 ; x 3 a) If f(x)= 2x-6 is continuous at x=3, then find the 2-5 ;x=3 value(s) of k. sinx b)…

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Q: Q1/ Solve the differential equation: dy x %3D dx 8y

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Q: Define. Show that h is continuous at x = 0 but h' (0) does not exist

A: Function is said to be continuous at a point x=a, when the function is defined at a and the limit of…

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: 1. (Bx2 |x- 61-8 for x> 2 (a) For what value of Bis the function f(x) = }", for x 2 continuous atx=…

A:

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: Show that f is continuous on (-0,00) sin x if x 4 V

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Q: Q3: Choose A or B (one only) (x2 + 2x lx³ – 6x if x -2 A) Check the continuity of the function f(x)…

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Q: x´sin÷, x0 Let f(x)= X X = 0 Examine the continuity and differentiability of f(x) and f'(x)at x = 0.

A: The solution is given below in the next step:

Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: 8. Intro To Real Analysis

A: (i) For f(x)=x2+2x2+3x−3​, the function is a rational function. Rational functions are continuous…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.