1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k. %3D

Q: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

A: 1) To find the largest interval on which the function f(x)=x+3 is conitnous.

Q: 2. Find the area bounded by the curve y = x³ – 3x2 from x = 0 to x = 2. -

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Q: Determinant of n x n Matrices. Solve for the determinant of the following matrices using (a)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The first along term of a sequence with a (ecursion formila e the lemaing terms for- B given beloN.…

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Q: Find the indefinite integral and check the result by differentiation. Step 1

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Q: 3. Compute f (x)dx f(x) = { 2x if x <1 4 if x 21

A: Given: fx=2x if x&lt;14  if x≥1 And I=∫04fxdx The Power rule: ∫xndx=xn+1n+1+C

Q: Calculate the iterated integral. 6. x/2 (y + y2 cos(x)) dx dy Need Help? Read It Watch It

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Q: Sketch the region enclosed by y = 7x and y = 3x". Find the area of the region.

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Q: 642 1. Consider the graph of y = f(x) below. State the value of each of the followin u do not need…

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Q: a 0 0 0 0b0 0 11. Using cofactor method, prove that det M = abcd %3D 00c0 0 0 0 d

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Q: (2x +3) dx x2 +4x +29

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Q: Sketch the region enclosed by a + y = 42 and a + y = 0. a) Favoring convenience, should you…

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Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: f(x) f'lx) %3D

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Q: da

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Q: 4. Find the integral of your answer in problems 2a and 2b. CO

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Q: What is the equation of the line that contains the vertices of the hyperbola (z+ 4)2 (y+2)² = -1? 16…

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Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE ANDCLEAN SOLUTION. (x – 2y + 5) dx - [2 (x – 2y) + 9] dy = 0…

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Q: x² – 2x – 1 dx (x – 1)2(x² + 1)

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Q: 5. Determine the values of x for which the function is continuous. x + 5 x² – 5x + 4 3x +1 2x2 – 8x…

A: a. fx=x+5x2-5x+4b. fx=x4-x2c. fx=3x+12x2-8x Note:     Multiple parts are given, we are answer only…

Q: 3 a. f(x) = V3x³ – 2 - b. y = (vx + 1)(x² – x) 2x5-3 c. f (x) coS x

A: a) fx=3x3-23b) y=x+1x2-xc) fx=2x5-3cosx Note:   Multiple parts are given, we are answer only three…

Q: Set up the definite integral required to find the area of the region between the graph of y = 18 – a…

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Q: 1. Find the value of the directional derivative at the particular point Po for the given function in…

A: Given that gx,y=y2tan2x ; U→=-32 i^+12 j^ ; P0π3,2We need to find the value of the dorectional…

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: Given; There 10 points in a plane such that no three points are collinear

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decinal places when…

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Q: A company estimates that it can sell 2,000 units each month of its product if it prices each unit at…

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Q: t Consider the DE r y"- zy'-8y 3r- A) Verify that y1 =x* and y2 = a satisfy the DE: a'y" - ay'-8y =…

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Q: EN tind an equation tor the line tangent to the Lurve at the point defined by the given t, Also find…

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Q: You want to construct a box whose height is twice the base length.  The material used to build the…

A: Here, let h be the height, l be the length and w be the width of the box. Then given that height, is…

Q: Sketch the graph of f(x) sketching the graph of a function. Label your graph. = -3r – 4x² + 6x – 2…

A: Function

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A: Please refer to the image below

Q: Evaluate the integral (Partial Fraction Decomposition) xdx (x² + 2)(x² + 1)2

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Q: Determine it the fellowing series coaverges or diveryes Give reasons tor Hi nti tirst Show that…

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Q: integral od pi/4 0 sin^5 θ dθ

A: A detailed solution is given below

Q: Sketch the region enclosed by y = e*", y = e", and x = 1. Find the area of the region.

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Q: eMx cos nx dx

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Q: Use the chain rule to calculate the first derivative of the following 19. (2x + 6)3 20. In (3x - 2)…

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Q: Use Green's Theorem to evaluate F. dr. (Check the orientation of the curve before applying the…

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Q: sin' xcosx dx

A: Indefinite Integration

Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: Solve the two items using Integration by parts. 1. (x' V9-x? dx

A: Question - 1:- Given: ∫x39-x2dx Formulas used: ddxxn=nxn-1ddxconstant=0ddxfgx=f'gx·g'x        Chain…

Q: 5. (4x3 — 6ху?) dx + (4y3 — 6ху) dy 3D 0

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Q: Evaluate the integral (Trigonometric Substitution) x*dx J (x² + 4)² 2

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Q: ,00 is deposited in an account with an interest fate of 1200 ) ith respect tor when r is 10.00%. dA…

A: Given query is to find rate of change of amount with respect to r.

Q: Evaluate the integral (2х — 8)dx - x2 – 6x + 18

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Q: the bot test to determine it the use tollowing series converges or diverges

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y®)Zdy

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Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: Find the equation of the tangent line to the curve y = 6 tan z at the point (, 6). The equation of…

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Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1