f(x) = 1 + 2 A X- 1 (A) (-*, 1) U (1, *) (B) x + 1 (C) all real numbers (D) (-x, 0) U (0, ) (E) x + 0

Q: The lower limit is less than 0, so part two of the fundamental theorem of calculus cannot be…

A: The second part of the fundamental theorem of calculus states If f(x) is a continuous function on…

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: Using the fact that Inſu(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=ln ux+ln vx

Q: using at the y-cc

A: Given equation is: xy31+y2=85 Then we get, 5xy3=81+y2⇒5xy3=8+8y2⇒5xy3-8y2=8 Differentiating both…

Q: tan"x jun's de - | tan"-x dx (n 1) n- 1 tan x sec" r sec x dx (n 1) n- 1

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Q: tionship between x and y.

A: Linear Eq: 9.x=1,2,3,4,5y=f(x)=2,4,6,8,102y=xSo, this is the requiredequation of line.

Q: 16. etan (1) sec² (x) dr

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Q: 3) f(x) = ln(x5 - cos²x) 5) f(x) = xsinx 4) f(x) = x² 1 + x³ 1 6) f(x) = x¹ tan- X

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Q: ax²-3 -,х> 1 x-1 Value of a and b that will make f (x) = continuous everywhere are ... lbx + 2, х <…

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Q: Find the derivative of the function. State the domain of the derivative. f(x) = [In(x)]6 f '(x) =…

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Q: tan x 1. Differentiate the function: Y = ea* In x

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Q: G. (CHAIN RULE) 1. f(x) = (3x² - 2x+4)² 2. y = sin 2x 4 (a² - y²)² 4. g(x)= (3x² + 4x - 5)5 3. 2 =

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Q: In 2x -dp-

A: To evaluate the integral: ∫2ln2xxdx Solution: Let substitute t=ln2x. Differentiating both sides, we…

Q: Leb Fur =ue Show thab f6/0 )c

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Q: theorem if Yet, I think I

A: 1. Ax=h+p 2.∀x.Ax 1.Universal Generalization on 3. Ax→∀x Ax  1,2 Introduction.

Q: Finding a Second Derivative In Exercises59–62, find d2ydx2 implicitly in terms of x and y. 59. x2y…

A: Implicit functions in 2 variables are obtained when both the variables are used to define the…

Q: f-1(x) = Verify that f(f-1(x)) = x and f-1(f(x)) = x. %3D F(F-1(x)) = f( %3D - 5 = x f-1(f(x)) + 5 =…

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Q: derivative of the firm's profit function is F'(x) = -0.03x2 + 3x - 100, where x > 0 is the output…

A: We will use the basic knowledge of functions and derivatives of functions to answer this question.…

Q: lim cos2x-1/sinx x-> 0

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Q: sechx+cshx b) prove that e2x cshx-sechx

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Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: Relation 3 {(;, w), (g, =).(w, -), (c, c)} O Function O Not a function

A: Given that : {(z,w) , (g,z) , (w,z) , (c,c)} Since , A= { z , g ,w ,c} B= { z, w , c}

Q: 6. Use implicit differentiation to find first order partial derivatives: tan-(x²y) = y²z3 +…

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Q: From algebraic form of function ez, prove that  |ez| = ex

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Q: Find the area in square units of the region under the graph of the function f on the interval[-10,5]…

A: By fundamental theorem of calculus area of square is A=∫-1055dx=5x-105⇒A=55+10⇒A=75 square unit

Q: function defined on [-1, 1] (a) (1 - x²)4 = (1 - x*) ^-21) Power Chain Rule with u 1-x 2(1 - x*)4…

A: Solve using chain rule of the derivative

Q: Finding the derivative of f(x) = 2x2+3x-1, using definition of derivative %3D A- В BIB:

A: Our objective is to find the derivative of f(x) using definition.

Q: Hn+1(x)= 2x Hn (x) – 2n H-- 1 (x) H,(x)= 2n Hn-1(x).

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Q: f(x) = sec x As x = π-/2, f(x) =  As x = π+/2, f(x) =

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Q: f) = In(tanx) -1 %3D

A: ddxlnarctanx

Q: Regioin bounded by x-g and X=24-9

A: Area bounded by the curves, Using the double Integrals

Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: 2 sinθ u - sinθ - 1 = 0,       0< u<2π

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Q: 1) f(x) = x5-x¹ + x² - x +² 2) f(x) = sin³x - e³x² + ln(1 + 5x²) 3) f(x)=√1-x² sin-¹ x 4) f(x)=√√x +…

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Q: Using the fact that In[u(x)v(x)] = In u(x) + In v(x), use the chain rule and the formula for the…

A: Given: lnuxvx=lnux+lnvxddxlnx=1x

Q: 5 - x2 + 2x – 3 = 0

A:

Q: Derivative - 16sin4x

A: Given: 16sin4x

Q: cos2r – sin2x cos2x For -dr=-F(x)+C What is F(x)? cosx – sinx 3 2 sinx + -cos'x+ cosx+ =sin³x 3 3 2…

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Q: sec2 x 2. csc2 x = %3D sec2 x-1

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Q: lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

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Q: continuous

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Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: sec-1(V2+h)-sec-1V2 (ii) ļim h-0

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Q: (sin(x), x 4 x, k(x) = f(x) = -x2 + 4x – 2, х — 6,

A: Consider the given function as fx=sinx     x&lt;0x         0&lt;x&lt;2-x2+4x-2…

Q: function with form y = ax

A: Given,  A power function y=axp passes through the points 3,781 and 6,71296. The equation of power…

Q: - the use write down Calculus in econamicd.

A: Use of Calculus in economics

Q: Simpson Rule. 2- x, (1, 3), n=4 3- x.sin(x), (0, 2), n=6 4- 1/(1+ x³), (0, 1), n=2, 4 ---

A: Since you have post multiple questions, according to our guideline we can solve only first one, or…