Find two functions f and g such that (f ∘ g)(x) = h(x). (There are many correct answers. Use non-identity functions for f(x)  and g(x).) h(x) =    5 − x

Q: Find g' (3) given that f(3) = -6 and f'(3) = 4 %3D (a) For g(x) = 3xr² – 5 f(x) %3D 1 g' (3) = %3D 2...

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Q: One of the following is an improper integral. - In 3 e* dx 4 – ex dx In 2 xV16 – In x dx cln 2 dx x ...

A: In this question we have to find the value of Improper Integral. Note: As per our policy we are supp...

Q: dx 3. The integral +1 reduces to where u = f(x) and for some constant k. Compute f(1). (a) (b) e +1 ...

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Q: 7. dx For the integral which of the following options is correct? A. lim (x – 1)½ |", + lim (x – 1)½...

A: ere, the given integral is: ∫-12dx(x-1)23 which is an improper integral of type 2 because the integr...

Q: Consider the function below. Is g continuous on (0,1]? on (1,4]? why or why not? if æ 4.

A: Explanation of the answer is as follows

Q: find a and b if the line tangent to f(x) = a(x − b)2 − 1 at x = −3 is also tangent to g(x) = 1/4(x +...

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Q: Find the first derivative of the given functions. A. Trigonometric Functions 1. y= sec? 0 – tan² ® 1...

A: As per our guideline we are supposed to be answer only A(questionp 1y& 2)part you can respost qu...

Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

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Q: Give a power series Cnx" such that it is convergent if |x| 1 of x = -1.

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Q: What is the accumulated value of periodic deposits of $4,500 made into an investment fund at the beg...

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Q: Find the average rate of change for the following function. f(x) = 2x - 5x +3 between x = - 1 and x ...

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Q: (9 – x² , x 10 [x – 4] (a) f(2) (b) f(12.5) (c) f(-3) (d) f(5) (e) f(1.5)

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Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n>1              ..(i) We have to show that Sn  is not an...

Q: If a <b_<c_ If lim a =L and lim c,=L+7 then which of these is TRUE? n- 00 O A By squeeze theorem, (b...

A: The correct option is,  

Q: Find the radius of convergence of the power series. (If you need to use es or -eo, enter INFINITY or...

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Q: Evaluate the integral S 4x4 – 12x² + 7 xdx (2x2 – 3)/4x4 – 12x² + 7 + 2ln|2x² – 3+/4x+ – 12x² +7]} +...

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Q: Solve the following differential equations. Indicate the (Differential Equations) nethod/s used at t...

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Q: 7Q b) TR = (Q+3)

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Q: Evaluate the integral cot 2x Xp- Vcot2 2x - 15 -금ArCsec Csc 2x +C A 4 -nlcot 2x + Vcor 2x - 15|+C co...

A: This question is based on indefinite integral.

Q: cSc x du 5. If u = f(x), then -. Compute f dx = sin x – cos x 2 (a) 1 (b) -1 (c) 0 (d) 2

A: ∫cscxsinx-cosxdx=∫duu

Q: Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 =0 ...

A: We will express the line L defined by y+3=3x and z+1=0 hyperbola -x2-2x+2y2+4y=-2 as a vector valued...

Q: ... The Factor Theorem states that if f is a polynomial function and f(c) = 0, then is a factor of f...

A: factor theorm states that  if f(a)=0 then, (x-a) is a factor of polynomial f(x)

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 3 P (X) –

A: Taylor polynomial of 4th order of function fx at a is defined as: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x...

Q: 2. (а, By completing the square, show that 1/2 d.x x2 – x +1 3/3 By factoring x³+1 as a sum of cubes...

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Q: Find the derivative of the function. X-1

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Q: Find two functions f and g such that (fo g)(x) = h(x). (There are many correct answers. Use non-iden...

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Q: 5. Solve a) In(x+1) = 3 b) e2 – e = 2.

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Q: u du Form Answer Ex. S 3+ 2cosx 5sinx 5 -5V3+ 2cosx + C dx 3+ 2cosx -2sinxdx ī du 3 15. Given: S -dx...

A: This is a integration problem

Q: Find the 10th term of a geometric sequence whose 2nd term is 7 and whose 5th term is 35. Report it i...

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Q: dx The integral | can be rewritten as V1. - X (a) lim (-2+2v1 – s) (b) lim (-1+2v1 – s) S--00 S--00 ...

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Q: 4. f(x) = (Vx)(x² – 2x) %3D -

A: 4. f(x)=xx2-2x Solution f(x)=xx2-2x      =x12x2-2x      =x2+12-2x1+12      =x52-2x32 Derivative of t...

Q: according to the squeeze theorem, for values of x near a if g(x)≤f(x)≤h(x) and limx→ah(x) = L then l...

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Q: Calculate the amount of money Kayla had to deposit in an investment fund growing at an interest rate...

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Q: ²+2x 5. Sketch the curve: y? x-1

A: The graph of the given function is plotted below.

Q: Evaluate the integral dx 2xx - 3x?

A: To find: The integral ∫dx 2xx3-3x23 Concept used: ∫1-v2+1dv=lnv+12-lnv-12

Q: In Exercises 39-42, the velocity v(t) of a particle moving in the plane is given, along with the pos...

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Q: 45-48. Average values Find the following average values 45. The average distance between points of t...

A: Here, the given disk is: R:{(r,θ):0≤r≤a} which is a circle x2+y2=a2 Therefore, the average distance ...

Q: A rain gutter is formed by bending up the sides of a 40-in.-wide rectangular metal sheet as shown in...

A: Given problem:-

Q: Use sigma notation to write the Taylor series about x = xo for the function. e*; xo = 6 6 2r – 6)* k...

A: Here we have to use sigma notation to write the Taylor series about x=x0 for the function f(x)=ex; x...

Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =...

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the numbe...

Q: While buying a new car, Jordan made a down payment of $1,100 and agreed to make month-end payments o...

A: down payment = $1100 duration of loan = 5 year 9 month = 69 month interest rate annually = 1%  so se...

Q: Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solut...

A: derivative

Q: Evaluate the integral cot 2x dx cot2 2x - 15 -금사 csc 2x +C A Arcsec 4 B -In/cot 2x + cot? 2x – 15|+C...

A: Here, the given integral is: I=∫cot 2xcot22x-15dx

Q: If a <b <e_ If lim a,=L and lim e,=L+7,then which of these is TRUE? - 00 - 00 O A. (b,) converges. O...

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Q: Evaluate the integral cot 2x S- Vcot2 2x – 15 V cot? 2x

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Q: Let S(x) 9 sin x + 9 cos x "(x) 3= r(-)-

A: Question is solved.

Q: 2022" + n 2022 (d) lim sin 2022! + n!

A: We have to find: limn→∞sin2022n+n20222022!+n!. We can take the limit inside of sin as the limit is o...

Q: e3x dx be given . If u = e* + 1, then the resulting integral is 2. Let ex + 1 | f(u) du. Compute f(3...

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Q: Use the binomial serles to find the Maciaurin serles for the function. 1 f(x) - (1 + x) Σ (x) = %3D

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Q: Find the nth Maclaurin polynomial for the function. 5x - 1 f(x) = n = 4 %3D x + 1 19 Pa(X) = %3D Nee...

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