Evaluate the pecewise defned funchan at the indicaked Values + 8if x4-1 1ラメッー if x >1 flx). f1-3) -15 (1-)F -7 f(0)

Q: 2. Max tries to simplify the expression (5x+2)(x+3)-(2x– 3)(x+3) as follows: = (5x+2)(x+3)-(2x–…

A: Given data is : Max tries to simplify the expression 5x+2x+3-2x-3x+3 Expression after simplification…

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: Show by contraposition that : Vx ERx?-7x-820 - x2 8 or x S-1

A: In this method, we prove negation of antecedent and get contradicted and get our required results.

Q: Show that $) it gly) 1-y 2

A: Recall: The domain of a function is the set of all possible inputs from the function.

Q: Find a counterexample to show that the statement is false. (Select all that apply.) x > 1…

A: If x is a real number greater than 1 then the statement x> 1/x is true.  But for real numbers…

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(-2) = 3.

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: 14x'y What is the simplified form of 2

A: To write the simplified form of the given expression

Q: find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

A: Derivative of function

Q: Explain how to use the evaluation part of the Fundamental Theorem of Calculus to compute L", (3r² –…

A:

Q: Compate the Cantiderivative of fox) = x²+4 xナ4 %3D x³+ax

A:

Q: 2. Max tries to simplify the expression (5x+2)(x+3)-(2x–3)(x+3) as follows: = (5x+ 2)(x+3)-(2x–…

A:

Q: (a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7…

A:

Q: Consider the following. Fx) = * f(x) 4 14 - 32x2 Find the critical numbers. (Enter your answers as a…

A:

Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

A:

Q: For f(x) = 7x2 - 7, find the number c in (-4, 4) guaranteed by Rolle's Theorem. (Use symbolic…

A: Rolle's theorem: If a function f is continuous on [a, b] and differentiable (a, b) such that f(a) =…

Q: -1 Ax) = 7xsin (x) f'(x) =

A: SOLUTION-

Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

A:

Q: (-5x + 4, for x 2 |1, Evaluate fl-1) - f(5)

A: Using the given function f(-1) = (-1)2 +3 = 4 f(5) = 1

Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

A:

Q: Show that f 1 (3) does not exist.

A: Given : To show f'(3) doesnot exists

Q: Suppose F(4) = - 1, - 1, %3D

A:

Q: Determine whether yy00 ory-y – ∞ as x-7-a∞ Ond x-7∞, 2 =x=-4x²-4x-8

A:

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: find of the f llowing 2. 2 -5x*

A: Solution of question is written in below steps.

Q: Give a proof by cases that [4x] = [x] + [x + ¼ ]+ [x + ½ ] + [x + ¾ ] %3D

A:

Q: 13) If x = 5a*, and a = 2b3, express x in terms of b.

A:

Q: The algebraic translation of "x is no more than 7" is

A: the algebraic translation of "x is no more than 7 " is ?

Q: A³ f2 = V³ fs 3

A:

Q: Find f') usig the deri vative rules. f@)= 4x2 +2x- 3 +2x -3

A:

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: If f(8)=4, f'(8)--6, g(8)--4, and g'(8)-1 and h(x)-5f(x)-3g(x)

A:

Q: Alice is in a 20-km running race. She always runs the first half at an average speed of 2 km/h…

A: Alice is in a 20-km running race.She always runs the first half at an average speed of 2km/h faster…

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

A:

Q: - 5/2+81 +81 주 lim x--00 2/12+Vt²–167 3

A: we will use the fact that any constant number divided by a very large number (infinity) we get the…

Q: The function f(x) = 4 for x < 2 and f(x) = 4 for x 2 2 has domain of all the real numbers. To True O…

A: As we know that domain is all the value of input (x-values) for which a function can define. for…

Q: Evaluate x2 - 2x for the value of x satisfying 4(x + 2) + -16 = 3x - 5(4 - x).

A: 4x+2+-16=3x-54-x⇒4x+8-16=3x-20+5x⇒4x-8=8x-20⇒8x-4x=20-8⇒4x=12⇒x=3

Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

A:

Q: 3,80lVe this equadioR by USE GalSian eli minalion- X-34+ 42 =1 2W-2X +f-1 2W -X -27 + 47=0…

A: Given system of equations:x-3y+4z=12w-2x+y=-12w-x-2y+4z=0-6w+4x+3y-8z=1To find: values of w, x, y…

Q: Do you agree with the contention that the funtions f(x) = x + 2 and g(x) = x2 -  4 ÷ x - 2 are the…

A:

Q: In False Position method, if f(xl) is

A: Given, In False Position method, if f(xL) is much closer to zero than f(xU), it islikely that the…

Q: 7. Determine whether the funcion is even, odd, or neither: f(x) = 1+x2

A:

Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

Q: The algebraic translation of "x is no less than 7" is .

A: Given statement is "x is no less than 7:. To translate into algebraic form. Solution: Given that x…

Q: 725 + 7z4-2r If f(z) , find f'(z) Add Work

A:

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: A let flx1 - 2ペ+7X+6 then Hien f(8) = P

A: f-1(x)  is the function which returns what value will function take for x.  Function is the unique…

Q: Express the following as a single-den 4 2 x² - 16 x + 5x +4

A: Follow next step