Given a2 +1, x<1 f (x) = 2x, %3D x > 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

Q: Compare the values of delta y and dy for the function f(x)= x^3 - 3 at x=3and delta x= 0.2

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Q: Given a continuous function f(x) 2 0 at [0, 1] and f(x) < 0 elsewhere, which of the following is not…

A: Given

Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

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Q: If f is continuous and q and h are differentiable functions, find a formula for d ch(x) f(t) dt dx…

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Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: Find the linear approximation to f(x) cos(x) at x = 0. O L(x) = O L(x) = 1 O L(x) = 1+ x O L(x) = 1…

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Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n?…

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Q: 45. For what value of a is Jx? - 1, x< 3 | 2ax, f(x) x2 3 continuous at every x?

A: Given: fx=x2-1,x&lt;32ax,x≥3 We know that given function will be continuous at every value of x, if…

Q: Assuming that z is a differentiable function of x and y, Let F(x.y.2) = In(x³y) – e" -tan-z. Find F,…

A: We can find the answer as below.

Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

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Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is R6 (the Right-Hand…

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Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: Suppose that f is a differentiable function such that f(0) = 3 and f'(0) = 12. Compute the value of…

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Q: Find the line tangent to the graph of f(x) = cos(x) at xo = T.

A: f(x)= cos(x)  Then, f(π) = cosπ⇒f(π) =-1

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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Q: Find linearization L(x) of f(x) = tanh=' at a= 0 and use it to estimate f(0.01).

A: Topic:- linearisation

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: SS()dt =x arctan x

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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: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

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Q: Q2/ Find the dirivative for the follwing function y = cosh(x)/ln(x)

A: Given: To Find:

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a ,b],…

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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: uppose ſ, f (x)dx = 8, f(x)dx = 10 , §' g(x)dx = 4 , fó g(x)dx = %3D %3D %D ind : f (x)dx 4 [f (x) +…

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Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of 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: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.

Q: '49 If f is continuous and f(x) dx = 18, find | xf(x?) dx.

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Q: Find a nonzero value for the constant k that makes the function tan(kx) x < 0 f(x) = Зх + 2k?, x 2 0…

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Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

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Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: The antiderivative of f(x) is unique. True False

A: Thus, The antiderivative of function is not unique, but is unique up to a constant.

Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: 10. Let L : R² → R be given by 2²–y? if x + y # 0 L(x) = L(x, y) = I+y 2x otherwise Decide whether L…

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Q: Find a nonzero value for the constant k that makes the function (tan(kx) x < 0 f(x) = Зх + 2k?, x 2…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = 1 a = 3 L(x) :…

A: The solution are next step

Q: If m < f(x) < M for a < x < b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: S() dt, where f is a continuous function, find f(4). (c) A 10 ft ladder rests against a vertical…

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Q: w(x) = |x + 1| m at x = 1 Select the correct response: Continuous Continuous

A: For continuous function LHL is equal to RHL and function values same

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

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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: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

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Q: Suppose that h is continuous and h (x) dx = 12. Solve for 2 4 h(v20–4x -dx. Hint: note that h (x) dx…

A: Given that ∫24hx dx=12. Put u=20-4x. Then, du=1220-4x12-1-4 dx On simplifying, du=-220-4x dx

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