Find the norm (or length) of v = <-2, 3)

Q: Consider the following functions. f(x) 3 Vx - 3 g(x) = x – 3 %3D Sketch the region bounded by the…

A: Let us first find the intersecting point. So,               x-33=x-3⇒x-3=x3-9x2+27x-27⇒x=2, x=3, x=4…

Q: Evaluate the iterated integral. /4 y cos(x) dy dx 地

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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Q: Evaluate (2x – y) dx + (x + 3y) dy. C: arc on y = x/2 from (0, 0) to (4, 32)

A: This is a problem related to vector calculus. Based on green's theorem we will solve the integral.

Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

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Q: Can you find the second subpart to this wue

A: This question has been solved completely. Please ask your query clearly.

Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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Q: Find the area of the region bounded by the given equations. Clearly state the integral(s) used to…

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Find the general solution to the ollowing differential equations: (A) y = 2yx(y'+3)+13x %3D

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

A: Given problem:-

Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: A detailed solution is given below

Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

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Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 7…

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Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

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Q: Given f(x) = 3x2 – 24x + 15, a. Write f(x) in standard form. b. What is the axis of symmetry of…

A: Given query is to write the standard form and find symmetry.

Q: 1. Find the volume of the parallelepiped PQRS if the vectors V(PQ), v (PR), and V(PS) are…

A: Given PQ=3i+2j-k PR=i-2j+3k PS=i-j+k. Volume of parallelepiped =[PQ PR PS]…

Q: Match the equation with its graph. 16 56

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Q: Determine whether the improper integral diverges or converges. In x converges O diverges Evaluate…

A: Here we have to determine whether the given improper integral diverges or converges.

Q: Find the exact length of the curve given by z = t° , y = t (0 <t< 4). Length

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Q: 3 if x 2 the one-sided derivatives of f at x = 2 whether f' (2) exists. If it exists, specify its…

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Q: In x 6. lim, x

A: Solution:

Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

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Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: Suppose the function f(x) is an odd function and lim, f(r) = 27. Use this information to evaluate…

A: For an odd function f(-x) = -f(x)

Q: Find div F and curl F if F(x, y, z) = 7y°z®i – 5æ³z10j – 7xy°k. 3„10. div F= curl F=

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Q: y" –3y – 2y=0; x =0,y=0, y' =9,y' =0

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Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

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Q: Consider the function y-2+3x² -x³ a) Find the intervals on which this Punction is increasing or…

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable 5. f(x) = 2x²…

A: Find your answer below

Q: х2 +7х — 3 (2х + 1) (х dx 2)² —

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Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 5…

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Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

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Q: View Policies Show Attempt History Current Attempt in Progress Your answer is incorrect. Find T(t)…

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Q: I.TRUE or FALSE: Read carefully the statements below. Choose A if the statement is ALWAYS TRUE,…

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: dx 3-x

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Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: 2. Find an equation of the plane containing the point P(0, –,÷) and the line determined by the two…

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Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

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

A: This question can be solved using the concept of domain.

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.