Determine the following Laplace transforms: (i) mathcal L \ cos^ 2 3t\ .

Q: csc z) Evaluate: lim (x² + e¬®)@¯

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Q: Q11. Which one of these expressions in words does not equal 1? A. The natural log, In of the natural…

A: To find the Expression in words does not equal to 1

Q: Use the Integral Test to determine whether the series > 'n² +1 is convergent or divergent. n=1 Show…

A: To determine whether the given series is convergent or divergent.

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i + 4 sin(t)j; t = 3 r() - () V3 1 T .3 2 2…

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Q: 5. Find the critical numbers, and the intervals of increase/decrease for y=ln(4-x) %3D

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Q: Sorry im running out of questions

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Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x²…

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Q: . Find f 6x5-25x*+8x3 +43x2-8x-12 (3x-11x3+9x2-11x+6)(9x2+12x+16) dx if this can be reduced to…

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Q: Clairaut's Theorem Let DCR be a disk containing the origin and assume that q : D → R is a function…

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Q: 2+ 12 40. Find all local extreme values of f(a) The FIRST local extreme value, moving from left to…

A: Find out the maxima and minima.

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Q: Evaluate F. dr F(x, y) = 5xi + 8yj C: r(t) = ti + v4 - tj, -2 sts 2

A: Calculate drdt. drdt=ddtti+4-t2j      =1i+124-t20-2tj      =1i+124-t2-2tj      =1i-t4-t2j…

Q: Yz01003 b00 Cos07+3 2. 7) 300 Sing Y=0.002 Ysine dr do dø

A: A detailed solution is given below

Q: I really need your help, just want a guide or like a script type how to explain this on class each…

A: Here, you have to find the area bounded by the loop of the given curve. The given curve is: y2=x5-x2

Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Given the v-t diagram, determine the acceleration in ft/s^2 and distance covered in feet at 12s.…

A: These are the following points , we have to go through first The area under the v-t graph is the…

Q: The total cost function is given by the fixed costs minus the variable costs. True False

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Q: 2. Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) logg (x) lim In(x) X00

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We have to find the limit

Q: 7) Determine the total area bounded between the function y = 1 – x between 1 and 1. -

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Q: latch the vector field with its graph. F(x, y) = yi -6 5 5 -5+

A: Given: F(x,y)=yi Find: graph of vector field

Q: 6) Determine the equation of the tangent line to y = x/x when %3D x = 4.

A: Equation of tangent line

Q: Verify Green's Theorem by evaluating both integrals dx + x² dy = // | da ду дх for the given path.…

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Q: For the linear transformation T: R* - R, T(v) = Av, find T(1, 0, 2, 3) and the preimage of (0, 0,…

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Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i+ 11 sin(t)j + tk; t= 2 T() - T N 2.

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Use Stokes' Theorem to evaluate F. dr. z = 4 – 22 – y? F(x, y, z) = 2zi + 10xj+ 3yk where C is the…

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Q: Use the principle of mathematical induction to show that the given statement is true for all natural…

A: Question number 6 has been solved as per the requirement of the student.   This question can be…

Q: In the integration of (csc 5t)(cot 5t) dt, what is the correct "u"? * cot 5t 5t csc 5t O (csc…

A: This question is based on indefinite integral.

Q: MP USING TOOLS Use a fraction or a mixed number to represent the tiT on a number line. Let 0…

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Q: Find the area between the innér and outer loops of the limaçon r = 2 – 4 sin .

A: This is a problem related to area of the polar curve. based on the graph of limacon curve we will…

Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We can solve as follows

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: The objective of the question is evaluate the indefinite integral using the Green Theorem.

Q: The revenue of an online retailer increases by $320,000 every year, this is an example of…

A: We will find if this is exponential.

Q: Find the area of the specified region. sec e Inside the dircle r 3 and to the right of the line r =…

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Q: Plot the point whose polar coordinates are given. (4, 9/4)

A: The objective of the question is plotting the point in the polar co-ordinates and choose the correct…

Q: Determine the area of the region bounded by x = y2 – y -6 and x = 2y +4.

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Q: Suppose that f is a function given as f(x) = - x² +x – 2. Simplify the expression f(r + h). f(x + h)…

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Q: r(t) = cos(Tt)i – In(t)j+ vt – 16k; to = 17 %3D Choose one▼

A: Given

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 3 1 lim tto0 2t2 +3' 2t (?,?)

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Q: determine the interval and radius of convergence 1 Z-3)2+"(n² + 1) (4x - 12)" n=0

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Q: Apply differentiation rules (PRODUCT RULE) to find the equation of the line tangent to the graph of:…

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Q: Q5. Which of these statements is False А. (а?)3 — а6 в. а?а? — а 5 2.3 a a2 С. a3 = a¬1 D. a + a' =…

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

Q: H.W: Evaluate the integral 1 1 1. || x²e*ydxdy o y

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

A: Given problem:-

Q: Evaluate the definite integral. Sols i + e*j+ t k at O e6 - 1 i+ 6 1 k i- i- (e 6 1 6 2

A: We know that integration of xn is xn+1/n+1. That is power rule of integration.     Here i attached…

Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation