Determine whether k(x) is continuous at r = 3, where x + 3, x < 0 k(x) = x² + 1, 0 2.

Q: 4. Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ]

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Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: #46

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

Q: Consider the function of that is continuous on the interval [-5, 5] and for which ſo f(x) dx = 4.…

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Q: Suppose that a continuous function g satisfies: 3 g(x)dx = 6 and | 9(27)dz = 9. 0, | z9(3z*)dz. Find…

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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: if f(x) is a continuous function at x = -6 * = 0, then a 1- cos4x x2 If f(x)= { a x = 0 r>0 16+Vx-4

A: a= 8.   See the attachment for the complete solution.

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: Find a and b such that f(x) is continuous at x=1. [x – 2] + a x 1

A: A detailed solution is given below.

Q: Find the Wronskian for the set of functions.{e3x, sin 2x}

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Q: Let f be a continuous function such that 5 √ (f(x) — 2) dx? What is the value of f(x) dx = -2 and…

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Q: Suppose that a continuous function g satisfies: g(x)dx = 42 and g(2x)dx = 3. %3D 2 Find æg(3x²)dx.

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Q: If functions ƒ(x) and g(x) are continuous for

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Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: The function f is a composite of two continuous functions: y = cos x and y = x 2, so f is continuous…

A: The function fx is a composition of functions y=cosx and y=x2and it is a continuous function.

Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2]

A: Consider the given function fx,y=3x2-2xy+y2-8y First, find the partial derivatives of the function…

Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: If f is continuous everywhere except at x = 2, then f(x +1) dx is not integrable. True False

A: To check whether the given statement is True or False."If f is continuous everywhere except at x=2,…

Q: Find the linear approximation to f(x) = cos(x) near a =- [Where L(x) = f(a) + f'(a)(x – a) ] 3

A: Solution: The objective is to find the linear approximation

Q: "For a continuous function f(x), defined on an interval a , b, we have d f(x) dx = f(x), dx a…

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Q: Find the local linearization of f(x)=x^(2) at 2

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Q: Let f(x,y)=3x2-2xy+y2-8y  Find the absolute extrema over [0,1]x[0,2].

A: We have f(x, y)=3x2-2xy+y2-8y find critical points ∂f∂x=6x-2y=0 ... (1)∂f∂y=-2x+2y-8=0  ...(2)solve…

Q: Let X be continuous with pdf f(x) = 3x² if 0 <x< 1, and zero otherwise. Find: (a) E(X). (b) Var(X).…

A: The pdf of X is given by f(x) = 3x2 if 0 &lt; x &lt; 1 Note : According to our guidelines we are…

Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

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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: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x&gt;0

Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: The limit of f(x) = sin(x) as x approaches t is O T/x n/2

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: (d) A function not continuous at 0 such that (f(x))4 is continuous at 0.

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Q: x + y + 1 f(x, y) = , x ln (y² х — 1 -

A: A function f=f1, f2, ⋯, fn is said to be continuous at a if and only if the all the components f1,…

Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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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: Find “a & b” if f(x)=x^2+4x+a x>0 ; f(x)=bx x<0 ; f(x)=f(0) x=0 is continuous at every

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Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

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: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

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Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

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Q: Find the linearization L(x) of f(x) at x = a. f(x) = sin x, a = 0 O L(x) = 3x + 1 O L(x) = 0 O L(x)…

A: L(x) = f(a) + f '(a) (x - a) where, L(x) is the linear approximation of f(x) at x = a. f '(a) is…

Q: Give a formula for f(x) given that f is continuous and 2 x +x* + 2 = f (t) dt t+ 2

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

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Q: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

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: Determine unknown constants a and b for which g(x) is continuous at x=1. [5x - 2 x 1

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Q: For all continuous function f: [0, +o] → R, a > 0 we need to prove that 2*f) dx = [ xfw)dx

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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.