(1) Let A = 27-J²+² D²³² = 11/1/201 + R² B = -3P + 25-R³₂ C = P²+5J²³ - 2K² 2] € = 42-3² 9. Find 35. + 25². E³² 3B-C b. AB X C. DF || Find the vector projection of È onto 2

Q: Show that g: R → R defined by g(x) = (x+3)³. (a) Prove that g is bijective. (b) Find the inverse g-¹…

A: to prove  g is bijective ,prove g is one one and onto.

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A: Please see the below picture for detailed solution.

Q: For ​f(x)=x4−4x3+9 find the following. ​(A)  f′(x) ​(B)  At x=−4 The slope of the graph of f is....…

A:

Q: Find the vertex form of the function. Then find each of the following. ​(A) Intercepts    ​(B)…

A: Given query is to find characteristics of the function.

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Q: (a) Sketch a graph of a function f such that: of' 0 and f" > 0, for x > 3. (b) Does the graph of…

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Q: 3) Determine whether the infinite series converges absolutely or conditionally.. 3a) 2 (-1) ² / ² 1²…

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Q: (a) Determine whether the series is convergent or divergent. Justify your answer in detail. 1 1 + =…

A: The given series, a) 1+12+19+128+......=1+113+1+123+1+133+1+..... b) ∑n=2∞-6n2n2+2n+12n. We have to…

Q: 6. Suppose that f(r) when > 0. Find df (r)/dr.

A: The given function is: f(x)=xex2

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A:

Q: | arctan x^)dx

A: Given integral:- ∫arctanx2dx

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A: To determine whether the given statement is true or not

Q: 13 Given the graph of f(x), graph y=f(x). List th domain and range of EACH graph and list the EXACT…

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Q: Problem 1 (a) Find the arc length function for the curve y = 4(x + 1)³/2 with starting point…

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Q: a. ∞ Σ n=1 4 2 5n+20n+15

A: given series is                ∑n=1∞45n2+20n+15then we have to check it is convergent or not  now ,…

Q: I. SOLVE THE FOLLOWING D.E. 1.) [D³ + 6D² + 11D +6] (yx) = 0

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Q: he length of a rectangle is increasing at a rate of 6cm/s and its width is increasing at a rate of…

A:

Q: Q10: If y² + x² = x² x-0 1-cos(3x) Q11: Lim (²+k dx² a) 3/2 x≤1 b)2/9 c) 1/2 d) 8/9 the values of k,…

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Q: Q1 find the domain and range of the following functions y= 1 + x V1-2x

A: According to bartleby guidelines we supposed to do the first one of multiple questionskindly repost…

Q: Q11:- If v=/e -X₁ 4t find ду at 8²v Əx²

A: v = 1te-x24t ∂v∂t = partial differentiation of v with respect to t. ∂v∂t = -12tte-x24t +…

Q: Q8: If y = 3x², x increases at a constant rate=2cm/sec at x = 5cm, then the rate at which y…

A: As per your request (8) Given that , dxdt=2 cm/sec , x=5cm find dydt=?

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A:

Q: (a) Find the arc length function for the curve y = 4(x + 1)³/² with starting point Po(0,4).

A:

Q: 3 + 5+7+...+ (2n + 1) = n(n + 2)

A: Given that 3+5+7+...+(2n+1)=n(n+2)

Q: Evaluate farctan (x²) dx as an infinite series

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Q: Q1: If the line 6x - 2y = 5 is tangent to the graph of y = f(x) at x = 3, then Lim b) c)-2 d) 3 Q2:…

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Q: If f(x) = 19 + 5e* + xổ. f'(x) = 5e* + Select one: O True O False Give your reasons then

A: To determine whether the given statement is true or false

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Q: Given the function f(x)=√x-h+k with a domain of (xlx 2-5, x = R) and a range of (yly 28, y = R),…

A: Given parent function f( x ) = xtranslated function f( x ) = x - h + k

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Q: Given that limã→ exp(x)—1 X = Answer: 1, find lim*- exp(5x)—1 X Enter I for ∞, -I for —∞, and DNE if…

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Q: 8. y' + y = 5 sin(2t), y(0) = 1 9. ty'y=t²e-t, t> 0 10. y' = 2y² + xy², y(0) = 1

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Q: Problem 5 (a) Find the area enclosed by the x-axis and the curve x = lnt, y = t² − 5t + 4.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 5. Solve the following initial value problem using Laplace transform method: y" +9y = 13e-2t y (0) =…

A:

Q: Given

A: Topic:- application of algebra

Q: If w=e" and u = √x² + y² by used approximate method aw² axay

A: Given So,          ∂2w∂x∂y=∂2∂x∂ye-u             =∂2∂ x∂ ye-x2+y2             =∂ ∂ y-e-x2+y2xx2+y2…

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Q: 7) Evaluate Staide Ja Faldy 76) 2b) Jeus 9x sin 5x dx

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Q: In the following question, enter 000 to say "does not exist" Use the First Derivative Test to find…

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Q: For the probability density function (pdf) {1.2(2². (2-3x+x²) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 O…

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Q: Use differentials to approximate 13.7. b Express your answer as a t C Answer where is the nearest…

A: to approximate √(13.7) by the use of differentials.

Q: Question 4 y" + 4y = 8 cos2x - 8e-2x y(0) = -2 y'(0) = 0

A: The given differential equation is: y''+4y=8cos(2x)-8e-2x ;           y(0)=-2  and   y'(0)=0

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Q: 8. Jorsen invested $3700 that earned 3% and paid $277.50 in simple interest. What length of time was…

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Q: √4-x S₁ S x ²² x ² (1-x² - y²) d y dx x

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Q: Use differential approximations in the following problem. A company will sell N units of a product…

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Q: If f(x) = 19 + 5e* + f'(x) = 5e +ẩx 3x7. 5. Select one: O True O False Give your reasons 31/3 then

A: Given So,       f'(x)=19+5ex+2x5'         =19' +5ex' +2x5'          =0+5ex-25x65         =5ex-25x65…

Q: Show a representation of f(x) = cos(x) using the sum of it taylor series at the center

A: