h.w 5 EXERCISES 1: Find the gradient of the function at the given poin 1. f(x, y, z) = x² + y² – 2z² + z In x, (1, 1, 1) | 1.

Q: 2. Sketch a graph of the integrand, shade the region in question and use geometry to evaluate the…

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Q: (1 + 4xy) dx dy O a. 8 O b. 7 Ос. 10 O c. O d. 9

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Q: 4x2 + 21x + 54 dx x² + 6x + 13

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Q: | sin rdr 3.

A: Here we have to solve the given integration by using integration by parts.

Q: Find the average value over the given interval. -X. y = 5 e [0,4] The average value is

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Q: Find a function of the form f(x) = a sin(bx + c) such that the graph of y 6f 5 4 BR E 37 2 2 -2 3 -4…

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Q: Find an equation of the circle whose diameter has endpoints (5, 1) and (-1, -3). O=0

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Q: Calculate the Riemann sum 2 txi Ax; for the given data. i=1 x2 f(x) = 7 + 3x; [-1, 2] is divided…

A: f(x)=x22+3x;   -1,2 is divided into six equal subintervals.

Q: Find f if f'(x)=2cosx+3x^2 +5/1+x^2 and f(0)=-1

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Q: 1. Let R be the region bounded by the graph of f(x) = 2x² – x + 2 and x-axis F31 between x = 1 and x…

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Q: How would you classify the sequence 0.45,0.045, 0.0045, 0.00045, ........... А. Arithmetic Series В.…

A: 0.45, 0.045, 0.0045, 0.00045,..........a1=0.45a2=0.045a3=0.0045a4=0.00045Ratios of two adjacent…

Q: Use the function value to find the indicated trigonometric value in the specified quadrant. Function…

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Q: 5. The initial value problem which describes the motion of a certain undamped harmonic oscillator is…

A: We have to solve the given initial value problem and find the amplitude, period.

Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

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Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

A: By using Newton's backward difference formula to find the approximate value of y-13 when…

Q: A rectangular lot has an area of 1600 sq.m. Find the least amount of fence that could be used to…

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Q: Problem 3 If the nth partial sum of a series E1 an is п— 1 Sn n+1 find an and E=1an.

A: The given data is: Sn=n-1n+1  To find the value of an and ∑n=1∞an.

Q: A bicycle's gear ratio is the number of times the freewheel turns for every one turn of the…

A: Let's find.

Q: Show that Q(V3, V3) = Q(v3+ V3) %3D

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Q: Q/ Convert the function ...... . a. to lincar. function: 1) y= ax²+ b 2 aX.+ 9. ....

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Q: The graph of f consists of line segments, as shown in the figure. Evaluate each definite integral by…

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Q: Hiwin If Z=R Cxxy)and u=x-y V=x-y show that %3D

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Q: The park across the street is to be treated to control a new algae that is growing on top of the…

A: Given, f(t)=y=25t²-300t+600 The given equation is that of a parabola. It is of the form,…

Q: 4. Express the following single logarithm: as a i) log3 54 -log3 6 ii) 2 In (5a’b) – In (125 aº b²)…

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Q: Consider the parametric curve given by x(t) = -2t and y(t) = t². (a) Sketch this curve on the…

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Q: Find the integration 3x2 - 8x +13 xp. x3 + x2 -5x + 13

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Q: xe dr dx J (1+x)²°

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Q: A particle moving in a planar force field has a position vector x that satisfies x' = Ax. The 2x2…

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Q: In Problem 15 of Chapter 9, this equation was used to find the surface area of a cylinder with a…

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Q: D03 Mathematics for Social Sciences I | S2 21/22 courses / ECON1003 | S2 21/22/ General / Graded…

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Q: 3) Chain rule: y = (3x2 - 3x- 2)2 1/2

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Q: Return Submit 40 year population (millions) 39 2010 36.5 38 2011 37.7 37 2012 38.2 A 2010 2011 2012…

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Q: 1 dx /9x² + 4

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Q: ALL of the following are not types of functions except. а. one - to - many b. many - to - one c.…

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Q: a) lim f(x) b) lim f(x) c) lim f(x) d) f(0)

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Q: a) Suppose that f(4)=3 and f'(4)=-5. Find g'(4) where g(x)=Vx f(x)

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Q: 4 8 Suppose the sequence {b1, b2, b3, ...} is given by {-1, , 9' 27 Which, if any, of the following…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y2,…

A: This question is based on finding equation of tangent plane.

Q: 3. nn'+n+lo nニ

A: We have to find if the given series is convergent or divergent.

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then f(x) dx : lim f(x;)Ax n-…

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Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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Q: 4. Calculate the flux of F = over the square shown below, oriented counterclockwise. SS (Px +Q, R…

A: We have to check given work on this problem write or wrong   But this work is wrong Because flux or…

Q: a) Find the area of the triangle with vertices A(-2,5,1), B(3,-5,-2) and C(3,2,-4) using vector…

A: see below the answer and calculation

Q: An identity matrix is represented by... . а. Нн-1 O b. HH-H C. H-H

A: Given

Q: After a new firm starts in business, it finds that its rate of profits (in hundreds of dollars per…

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Q: Consider the function below. f(x) = V x2 + 7 - x (a) Find the vertical asymptote(s). (Enter your…

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Q: | 2f(x) + ldx

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Q: Simplify (/ da + dx ) completely. - 1 x2 t2

A: Given problem:-

Q: Find the area of the shaded region. 160- (5,150) f(x) = x - 8x + 21x2, g(x) = 20x + 50 (-1,30) 10

A: Given,            fx=x4-8x3+21x2 , gx=20x+50           To find : Find the area of the shaded…

Q: y A y = f(1) 4. The graph of f(x) is shown in the figure. Let A(x) = Lf(t) dt and F(x) = S* f(t) dt…

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