a. Find the value of (k) that make the fumction flk) = ,continuous atx = 0 +3k-3 x=0

Q: #46

A: We need to find the value of b such that the function g(x) is continuous at every x,

Q: Find the value of c that makes the function continuous at x = 0. SNIPP

A: Hence it is given that the given function is continuous, so we can write:…

Q: Suppose that h(x) has a continuous derivative h'(x), h(0) = -2, h(T/4) = 2 and tan(x)h'(x) dx = 4.…

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Q: Match the graphs A, B, and C shown with the functions ƒ(x), ƒ'(x), and integral

A: Given : The graphs of f(x) , f '(x) and Anti derivative of f(x)

Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: Let xª sin , x + 0; f(x) ={ 0, x = 0, where a > 0 is a parameter. 1. For which values of a is f(x)…

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Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: sinkx) x 0

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Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: Determine f(5) if f is a continuous function that satisfies +sin(a) f+sin(a) f(t)dt = 22² for all x.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Theorem 9.2.1 to show that T is not continuous at 0, no matter what value is chosen for b.

A:

Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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Q: 2. If f is a continuous function such that S(t)dt = cos(2x)e* - [e s(t)dt for all x, find an…

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Q: iii. is continuous at a provided g(a) # 0.

A:

Q: Suppose that  ff"' is continuous and f'(c)  =f"(c) =0 , but f"'(c) >0. Does f have a local…

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Q: define the function at 5 so that it becomes continuous at 5.

A: First, we rationalize the function, so that it becomes continuous at 5 which is shown on the board

Q: If the continuous RV X has pdf f(x) = (x + 1), in – 1 < x < 2 and 0, %3D elsewhere, find the pdf of…

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Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: Show that the subtangent of f (x) = ex is everywhere equal to 1.

A: Formula to find the subtangent of the function helps to find the required subtangent. Derivative of…

Q: attached

A: Linearization of f(x) at x=a is given by

Q: Consider the following function: f(x, y) = {xy cosy/3x2 + y2     if (x, y) 6 not equally to (0, 0)…

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Q: 1. Integrate the following functions over th given interval by using the extended trapezoidal rule…

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Q: 3) See the attached file -1 Vx-1 ,xs 2 ,x > 2 3-Let F(x)= is the function continuos at x=2 A)…

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Q: 3) Find a value of c for which f(x) is a pdf on the indicated interval. Q11 f(x) =, [0, 1] 1+x2

A: We know that the total probability is always 1. Using that we get:

Q: 4. Determine the set of points at which the function is continuous. cos(xy) b) f(x,y) = e? – y? '

A: we have to determine the set of points at which the function is continuousgiven function,…

Q: At which point c does g have a removable discontinuity? How shouldg(c) be redefined to make g…

A: Removable discontinuity- if right limit gc+0 is equal to left limit gc-0 is not equal to gc, thengx…

Q: Consider g(x) = rº/3. Is g(x) differentiable at x=0? Is g(x) continuous at x=0?

A: We find g'(x) using the power rule  Then we find the left and right-hand limits of g'(x) and g'(0)…

Q: The graph of a differentiable function f on the ir [2,10] is shown. Find the trapezoidal approximat…

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Q: Find the si0pe of the given Function メト at メ= y' 1.) u= Vler*) at x = 2) 4= In(3メ-2) a+ x= こ %3D

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Q: b) Show that the function sin for æ e (0, 1] { f (x) = for æ = 0 is absolutely continuous on [0, 1].

A: Function is called continuous function if the left and right hand limit values at each and every…

Q: Given a2 +1, x 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

A:

Q: Consider f(x) - x In x. The step size, h, of Trapezoidal rule required to approximate ) dx within an…

A: Given: fx=xlnx Then, f'x=x1x+lnx=lnx f''x=1x Now observe that f''x≤1, for all x

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

Q: Let g be a continuous function. Using the substitution u = 3x – 1, the integral (g (3x – 1)) dx is…

A: We can use the concept of method of substitution in order to solve the given problem.

Q: f is continuous and f(x) dx = 8, find xfc

A: we have to find

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: 3. Suppose at t minutes, r(t) meters is the radius of a circular oil spill from a ruptured tanker…

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Q: (E) f is defined at xo , where the value of 8 exactly is Q2. Let f:R → R be a function such that…

A: Q2. It is given that,f(x)=xsin(1x) has a limit at x0 not equal to 0.

Q: (b) Calculate f(z) dz. (c) Why did we show that the right hand limits at 0 = 0 of the real and…

A: Let us start solving the problem step by step

Q: - For what value of b is Sx, bx?, x2 -2 x<-2 х, g(x) = continuous at every x?

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Q: Suppose that the p.d.f. of X is as given f(x)=4x-1 for 0≤x≤1 and 0 otherwise Find the pdf of…

A: The probability distribution function of Y is:…

Q: j(x) = v2x – 4 %3D

A: We have  jx=2x-4   Function is continuous when 2x-4≥02x≥4x≥2

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: Prove f (x) 1+ mx is continuous at x = 1, where m e R

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Q: Graph the function and observe where it is discontinuous. f(x, y) = e1/(x - y) fis discontinuous at…

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Q: a non zero valie for the constant k that makes the fmction ww m tan(kx) x< 0 f(x) = 3x + 2k?, x 20…

A: To find a non zero value for the constant k that makes the function…

Q: Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl &lt; 2 b - x 2 for…

A: Given, hx=x+1x&lt;22b-x2x&gt;2

Q: d) Will h(t) be continuous or discontimuous at t = 3 if we use A = 1? If discontinuous, what type of…

A: Here we use the definition of continuity of a function at a point. Which is defined by Left hand…

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.