Consider the polar curve r = sin(3θ). Sketch this polar curve on the interval 2π/3 ≤ θ ≤ π.

Q: 1 n Prove that 1+ 2+ -3+ + 2-1 (Hint: Differentiate both sides of the equation equation.) +4. 1 1-z…

A: The solution is given below

Q: Given tan theta = 1  evaluate (without using a calculator): cot (90º - theta)  and  sec theta

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Q: 10.) What is the largest slope of y= x² x² +1 on [0,10]

A: Given  y = x2x2 + 1 slope = dydx

Q: If f(1) = −13 and f′(x) ≥ 31 for x ∈ [1, 11], how small can f(11) be?

A: Given query is to find the smallest possible value of f(11).

Q: x -4 2 lim x 2 x O a. 2 O b. -2 O c. -4 O d. +∞ O e. 0 O f. O g. 1 O h. None among the choices. O i.…

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Q: Given f(x, y) = = − 5x¹ + x²y³ - y, find fa (x, y) = fy(x, y) = fxx (x, y) = fay(x, y) = fyr (x, y)…

A: Given  fx, y = -5x4+x2y3-y6

Q: Sketch an excellent graph for the following equatic a) r = 2 cos(0) + 1 3π/4 TT/2 21 31 π/4

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Q: 1. Consider the vector-valued function R(t) = 't² - 3t+2 t² + t-6 Find dom R and lim R(t), if this…

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Q: 1. A 20-inch long wire is cut into two pieces (not necessarily of equal length). One piece is bent…

A: A 20-inch long wire is cut into two pieces (not necessarily of equal length). One piece is bent into…

Q: APPLIED CALCULUS (UPVOTE WILL BE GIVEN. PLEASE WRITE THE SOLUTIONS LEGIBLY. NO LONG EXPLANATION…

A: We need to find out the vertical and horizontal asymptotes.

Q: Write the function f(t) - {t F(s) = in terms of unit step functions. Find the Laplace transform of…

A: We know  ft=h1ta≤t<bh2tb≤t≤c  Then  ft=h1tut-a-ut-b+h2tut-b-ut-c

Q: Find the volume of the solid enclosed by the parabolics Z= 4CX²+y²² Jand 2 = 32- 4(x² + y²)

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Q: Find and classify the critical points of z = Local maximums: Local minimums: Saddle points: (x² -…

A: Multivariable calculus

Q: 1. Evaluate following integrals. COS I [(-2e - cos r) [(1-3) √6t-1² dt. a. b. C. c. [√ ln(x) da a)…

A: 1) a) The given integral is (pi/x -2e-cosx) b)(t-3)sqrt(6t-t2) c) sqrt(x) ln(x) Repost the next…

Q: An equation of an ellipse is given. 3x^2+y^2=9 Find vertices, foci, and eccentricity

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Q: 184. Use Green's theorem to evaluate line integral z²ydä – xy²dy where C is a circle x² + y² = 4…

A: The given line integral is: ∫C x2y dx-xy2dy     where C is: x2+y2=4

Q: 36. p4 0 (4-t) √t dt

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find the area enclosed by the ellipse z=3 cost, y=2 sint, 0≤t≤ 2m.

A: We need to find area enclosed.

Q: Explain Transformations of Trigonometric Graphs?

A: Transformation of a trigonometric graph: when the graph changes its position. like reflected about…

Q: Given the following graphs, find the area of the shaded region.

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Q: Find the measure of an angle θ that is coterminal to an angle measuring -420 degrees such that…

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Q: Test the convergence of the following series a) Σınte-n? n=1 b) En=2 In(n!) 1 ) Σ1 3*n! ηπ

A: We have to consider the given series are convergent or divergent according to the given series

Q: e [√²²₂ d. Using part (c) and by change of variable with u = e, evaluate √ere dr

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Q: The final should be 4 no? Not 23/6?

A: Given Vector:- F→x,y,z=lnx+y+xzπ,1+yzsinhy,zey-cosz

Q: 4. Let S be the surface in R³ defined by x² - y² + 2z² = 9. (a) Write down the equation of the…

A: The equation of the Tangent plane to the surface z = f(x ,y) at the point (a,b,c )is…

Q: If f(x) = = x+1 1, then 2 (fof-¹) (−2) = x-2' O a. 1 O b. -2

A: Given f( x ) = ( x + 1 )( x - 2 ) let f( x ) = y y =  ( x + 1 )( x - 2 )

Q: A house was valued at $100,000 in the year 1988. The value appreciated to $165,000 by the year 2004.…

A: A house was valued at   $100,000 in the year 1988. The value appreciated to $165,000 by the year…

Q: suppose San and Στη are series with positive terms and b is known to be convergent. (a) If an> bn…

A: We are given two series with positive terms ∑n=1∞an and ∑n=1∞bn, where ∑n=1∞bn is convergent, i.e.,…

Q: Find(rr) r d d/ (1₁•1₂) if x = ( 2 ₁ √ ². e²¹ ) and r₂ = (7, In (2),1).

A: Solve the following

Q: 5. Shade in the area given by the integral y² dy. 1 y = √ I

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Q: Given that S² ƒ (x) d x = 5, evaluate f² ƒ(x) dx.

A: Given,            ∫37fxdx=5To find : Evaluate ∫73fxdx

Q: BASIC MATH! UPVOTE WILL BE GIVEN! Answer in paragraph form. Describe the graphs of the equations:…

A: Let's solve graph equations given characteristics.

Q: If f is an even function, then f1 exists. True False

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

Q: the intervals on which f is increasing and the intervals on which it is decreasing. f(x)=6-x+x² ect…

A: Given query is to find the interval where function is increasing and decreasing.

Q: Solve the following DE: y'=y-xy³e-2r O e²¹ = y(x² + C) 2x O e²x=y²(x² + C) -2x = y²(x + C) Oe-2x =…

A: To find solution of given DE.

Q: Scenario: Students are taking a right cylindrical can with capacity/volume, e.g., a soup can, paint…

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Q: Find the area of the shaded region. 2 f(x) = 10x -3x²- -x. g(x)=0 1 6

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Q: Find the equation of the line tangent to the graph of f(x) = 3x - 1 at x = 0. O a. m = = 3 O b. y =…

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Q: 3 4. sec 0 = Determine: a. sin 0 and 0≤0 < 2л, b. tan 0 c. Possible values of

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Q: 8. Evaluate the integrals below. a) 27 3 •3√x X. dx b) 2 (80x√x + = 17) dx = (1+²+3 -1 2 X x-3 + +27…

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Q: Let L be a relation on R such that for all x and y in R, x L y if and only if x < y. Give a counter…

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Q: 1. Let C be the parametric curve defined by dy d²y a. Find and dx dx² [x = tan-¹t Y | = | ln(1 + 1²)…

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Q: Find the limits of the following vector functions. -2) 21³-t² tan (21) 21²" (i) (ii) lim In 1-0 5t…

A: Since you have posted multiple questions, we are supposed to answer only first  question. If you…

Q: Find the length of the arc of a circle of radius 4 inches subtended by a central angle of π/6…

A: Given  Radius of a circle (r) =4 inches central angle(θ) =π6 radians   length of the arc of a circle…

Q: dy 2 (1+x)=x²2y, given that x = 1 when y = 2. dx 3 x³ + (y + 1)² dy = 0 dx dy #cosy+(1+e*) siny dx =…

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Q: Question 4: Find the intervals on which f is concave upward or concave downward, and find the…

A: We need to find inflection point and concavity interval. As per Bartleby guidelines we can solve one…

Q: lim, 0 sinx − x 3

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Q: 6.25x² +9y2: = 225

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Q: Express the sum without using sigma notation. Simplify your answer where possible. 210920(+1) log10…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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