1. Find the lim f(x), value of f(-1). Is the function continuous everywhere? If not, where is it x→-1 discontinuous? What kind of discontinuity is it? 5 V= f(x) 3 -4 -3 -2 -1 1 2 3

Q: 4 4 Use the transformation u= 4x + 3y, v=x+3y to evaluate the given integral for the region R…

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Q: 2x dx 4e2x –8eª +5 e

A: To evaluate: I=∫e2x4e2x-8ex+5dx=∫(ex)24(ex)2-8ex+4+1dx=∫ex4((ex)2-2ex+1)+1dx=∫ex4(ex-1)2+1dx

Q: 1. Find the total differential dw. 2. w = re2u +e-V

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Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

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Q: 2у — 4 dy 2 + 49 с.

A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: Problem 5 3 For the function f(x) on the interval [1, 5], answer the following questions:…

A: According to guidelines,  We must answer only 3 sub-parts of multipart question given. So I have…

Q: 4e". se"ts dx de Let u* 2e*+2, e*. 2 dy =2e*dk 4 du - edx dx 4 p- du hp: T A 3 4 I du Ju 4 du A9 Let…

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Q: 4 y = ,x = 1,x = 4, and y = 0 is revolved about the y – axis. (Answer: 24n c. u.)

A: This question is based on finding volume of solid.

Q: Solve the following initial-value problem. f′(x)=2 3√x+3x^2, f(0)=6

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Q: Using concepts from this unit, Curve Sketching, of this course only, explain why a quadratic…

A: To explain the correct reason.

Q: 3) (0,1,0), (2,1,0), (3,4,7) Ans. Indepena

A: Given

Q: By considering different paths of approach, show that the function below has no limit as…

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Q: Select the correct answer. What is the value obtained by using left endpoints with n= 4 subintervals…

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Q: 5) Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0.…

A: For the solution follow the next step.

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: If on V = R² define the usual scalar multiplication « (x, y) = (« x,x y) , and addition (x1, Y1) +…

A: Concept: Vector space: Vector space is defined by the associative and commutative laws of vector…

Q: What are the direction numbers of a line given by the parametric equation:  x=6+t,y=5+4t,z=1−2t

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Q: .C find the firet order parhal dervohve f 4.5 1. z) = e 32 W="y - 10y2³ + 432 hCs, t) =° t?In ts) +…

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Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

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Q: A. Assimilation (Time Frame: Since we already presented S sin x dx and ſcos x dx, we can now do the…

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, Y, z) = 4.x + 2y + z subject to æ? +…

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Q: Section 3.2 In Exercises 1-3, (a) compute the eigenvalues and the associated eigenvectors; (b) for…

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Q: 1. Evaluate the following integrals. 2" – 4" - dy - с. 2+ 49

A: To evaluate the given integral.∫2y-4y2+4y dy

Q: Find a formula for the nth term of the sequence 1, - 4, 9, – 16, 25, ..

A: We can find the nth term of the sequence. We notice pattern of the sequence.

Q: 4-P(1+) che model A=Pe or A=P|1+- ] ,where A is the future value of P dollars invested at nuously or…

A: we have to find the interest rate

Q: Two lines have equations L1: (0,0,1) + s(1,-1,1), s e R and L,: (2,1,3) + (2, 1,0), e R. 10. What is…

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Q: Sexe" ds, C is the line segment from (0, 0, 0) to (1, 2, 3)

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Q: x² – 2x – 1 dx I ( – 1)²(x² + 1)

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Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

Q: Select the correct answer. The graph of the function fx) = x3 defined over the interval [0, 1] on…

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Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

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Q: aluate the function. Give the exact value. cos tan(V3) -1 cos(arctan( V3% = 0.5

A: Given query is to find the value of the expression.

Q: Sketch the region of integration and evaluate the integral. 1 y || 15y5 e xy dx dy ... Sketch the…

A: To sketch the region of integration and then solve the given integral.

Q: Find the linearization​ L(x,y) of the function at each point.  f(x, y) = x2 + y2 + 1  a) (1,2) b)…

A: L(x,y)=f(a,b) +(x-a)fx(a,b)+(y-b)fy(a,b).

Q: What is the absolute minimum value of the function f(x) = x' - 3x² on the interval [-2, 4] ? a. -4 O…

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Q: parhod derivohve of 4,5 43 6- 13

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Q: A. Find the area of the plane region bounded by the given curves 1. y = x, y = 2x, and x +y = 6…

A: Note: As per our guidelines we are restricted to solve only one problem. Please upload separately…

Q: 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in the form of…

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Q: .5 dx Vx4 – 2x2 + 1 b. 3

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Q: You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will…

A: We have to find the dimensions of the cylinder.

Q: Determine the angle between OR = (1,-2,3) and OT = (5,-3,2) %3D

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Q: Find the arc length when y = 2 ln(sin ) and /3 << x < T. %3D

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Q: Solve the system of equations (only real solutions) by the elimination method. Check your solutions.…

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Q: explain

A: We will check whether fundamental theorem of calculus applies.

Q: What are the two values of k closest to 1 - 4 for which S sin? (x +4) – cos² (x + 4) dæ has a value…

A: The solution is given in the next step.

Q: (b) Find the values of a and b so that the function f(x) = x² + ax + b has a local maximum at the…

A: Given

Q: ind the values of a and b so that the function = x + ax + b has a local maximum at the (-16,- 12).

A: We will find the value of a and b.

Q: On what interval(s) is f'(x) increasing? Decreasing? Explain.

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Q: y 10 X -5 5

A: Range is all the possible value of y that is output of  defined x

Q: Current Attempt in Progress 9. Find f(2x + 4)dx if f(x)dx = 3. Enter the exact answer. f(2x + 4)dx…

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