Solve the inequality for u: µ – x| < Vn (Do not rationalize the denominato)

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

A: We will solve this question by  differentiating f(x) and then finding the intervals for which the…

Q: Consider the cubic function f(r) = ar³ + bx² + cr + d, where a ± 0. Show that f can have zero, one,…

A: Given cubic function fx=ax3+bx2+cx+d where a ≠0

Q: The fuction f(x)=[x] is contionous at a=0 O True O False

A: a function is contionous if right hand limit and left hand limit is equal to functional value at x=0

Q: Given f (x) =r - 4r defined over [1, 3]. Using Secant :method, the first approximated root for f(x)…

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Q: B-Test and proof the function So (x In x)² dx

A: ∫01(x logx)2dx=∫01x2 (log x)2dx use integral by parts, ∫udv=uv-∫vdu u=(logx)2…

Q: a. Find the value of (k) that make fhe fimction contimuous at x = 0 3k -3 =0

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Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: sketch f(x)=sec x over the half-open interval -r,27). 2 1 3/% 27t 52

A: Given query is to find sketch the graph of sec(x) .

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: Find the critical numbers of the function f(z) = 2x'-24r. Answer (separate by commas): I = Il

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Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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Q: f(x) In(x² – 6)' at X = +2

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Q: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

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Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

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Q: Use Taylor's Inequality to estimate the accuracy |R3| of the approximation f(x) at the number a = 0,…

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Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: The absolute maximum of f(x) =x² – 4x on [0,3] is y= OA. OB. 4- o 3- OC. OD. 0.

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Q: attached

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

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

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Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: t 0, if x is irrational 1, if x is rational ve a rigorous proof that f is not integrable on the…

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: Let f(x) = Q[x] be a irr of prime degree p. If fr non-real roots then th

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Q: The range of the finction f(x, y) = In(-x² -+1) is %3D None of these O (00:0] O [0; +0) O [0;1]

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Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

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Q: 2. Suppose that f is a measurable function satisfying m({r €R: [f(x)| 2n}) < ne N. n3' Is f…

A: Given that f is a measurable function, with the following condition satisfied. m(x∈ℝ:…

Q: Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

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Q: Q3) For what values of a and b are -x² + a , x< 0 1 xsin-+1 , 0 < x< y = bx³ + 2 , Continuous at…

A: See the attachment

Q: Let x have the pd F F(X)=4x² else where. Find the vari ance of X=

A: Given that f(x)= 4x3 , 0&lt;x&lt;1 And 0 elsewhere. We have to find the variance

Q: Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x…

A: See the attachment

Q: Which values of C makes r(x) (a) left-continuous, (b) right-continuous (c) continuous x2 +3 for x 2

A: If the function r(x) is left-continuous, then use limx→-1-rx=limx→-1+rx, to determine the value of…

Q: | Are fi(x) = x and f2(x) = x² orthogonal on [-2, 2] inter- val? Find c and c2 so that f3(x) =…

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Q: O Show that the function f: N2 N defined by f(x, y) = 2X3Y is injective but not surjective.

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Q: 9. 3x2 Let g(x) = -2x2 r<0 (b) Prove that q is not differentiable at 0.

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Q: Q2 Let f(x) = 2x3 – 0.0064x² – 1.5x + Ia (a) Indicate that f(x) = 0 has a root in the interval [-3,…

A: let fx=2x3-0.0064x2-1.5x+Id where Id=0.55 (a) indicate that fx=0 has a root in the interval -3,0…

Q: The range of the finction f(x, y) = In(-x2-+1) is %3D None of these O (-00:0] O [0; +0) O [0;1]

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Q: let f (x) =- , over the interval 0<x<2n , find b 1 a O n 1 b O пп 1 1

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Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: Find the linearization at x = a. f(x) = sin°(x), a = 4 (Use symbolic notation and fractions where…

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Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8

Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

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Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

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Q: O De fine fG) in a way that extends g8) = X -3 to be continuows at x=3

A: It is continous function  problem.

Q: The solut (Туре yoL

A: This is a question on inequality from graph