4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x² - X - 2 6x² 11x +3 8x³ - 27 (b) lim x+3/2

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: Which of the following is not true? 4dx 4dx A S.. lim √x(x+6) c √x(x+6) 5 dx dx So 25-x² B = lim…

A: We have to find out the option

Q: f and g are continuous on [a,b], then [* Grix)g(x)]dx = [(* F(x) dx)(√° xXx) dx) g(x) A True B)…

A: We will solve the problem

Q: At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship…

A:

Q: Give the following infinite sum and limit: 8 2n-1 3n+2¹ n=4 a) rsin r (b) lim 20 x² + e²-1

A:

Q: How long will it take for an investment to at least double its original amount if it is growing at…

A:

Q: A bicycle with 20-inch diameter wheels is traveling at 17 mi/h. Find the angular speed of the wheels…

A:

Q: Given the function y=f(x), y" is found to be negative over the interval (4,8), then over this…

A: Answer is given in next step.

Q: x6 cos(x³) (A) True (B) False |dx=0

A: We will solve the problem

Q: Find the slope of the tangent line to r²e³ + y²e² = 2e at (1,1).

A:

Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: All Option are  correct So we have to choose Option 'A'

Q: Find the area bounded by y=e*, y=lnx, x=e, the x-axis and the y-axis. (A) 13.1543 B) 13.1435 C)…

A: Given problem:- Find the area bounded by y=ex , y=ln(x) , x=e, the x-axis and the y-axis.

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

A:

Q: 1²₁ (886x5)) dx = 0 cos(x3 A) True B) False

A: Answer is following.

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A:

Q: Question 36 To integrate x³ ex dx, we apply integration by parts and in the form u dv, dv is set as:…

A:

Q: Determine the values of a for which the system has no solutions, exactly one solution, or infinitely…

A:

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

A:

Q: Hewlett Plastics Inc. received a loan of $57,500.00 at 3.75% compounded quarterly to purchase…

A: We know formula for compounded interest:A=P1+rnntwhere A= Principal amount +total interest amount,…

Q: 10. State whether the following series converge or diverge. Justify your answers. (b) Σ (# + gr)…

A:

Q: Find the exact solution for e2x−4ex−32=0.   If there is no solution, enter NA.   Enclose…

A: Please follow the next step.

Q: All continuous functions are integrable. A) True B) False

A: Solution:

Q: The population of a city is modeled by the equation  P(t)=335,242e0.25t where tt is measured in…

A: Basic properties of ln are used

Q: Evaluate L L ³ xy² 1 3xy² dy dx.

A: SOLUTION-

Q: Which of the following is not true? 5 dx dx ® (Α Sº o 25-x² lim c+5-0 25-x² ® √ in(x²) dx = lim_…

A: We have determine the integration

Q: xp zx — 9L^gx f

A: Evaluate the ff. by integration by parts.

Q: Which of the following is not true? A √ in(x²) dx = lim_²in(x²) dx А ₂3 3 dx dx B S²³² √₁ In(x²)…

A: Just use the definition of improper integral of first and second kind and find the required…

Q: Find the area that are bounded by: y=x²+5x and y=3-x² from x=-2 to x=0.

A:

Q: Which of the following is not true? A None of the given choices .3 dx dx S₁ in (x²) B lim S c+1+³c…

A: Let's solve.

Q: Q2. Find the exponential Fourier series for f(t): (1 = Fourier series. 0<t<1 (2 1<t<2 then find the…

A:

Q: f:R+ → R f is a strictly decreasing function. 3 1 f (x) · f ( f(x) + 2x 4 f (9) = ? 1) 3) 1 6 4) 1…

A: Answer is given below.

Q: 1. f(1-cot 2 x)² dx

A: Solution:

Q: B.) For numbers 1 to 10: Determine if limit of each function exist using the piece-wise function…

A:

Q: Q: 1 the first derivative test to find the intervals on which the function f(x) = xe-* = is…

A: Given, f(x)=xe-x

Q: Find the length of the curve of y=x³/2 from x=1 to x=4.

A:

Q: Find the determinant of the matrix, O22-122-13 O22-12A +13 O²+12+13 02-13 2-11 4 6 2-1

A: Topic = Determinant

Q: 6. f In² x dx

A: Topic = Integration

Q: Solve the differential equation: (2x - 4y - 3)dy=(x-2y)dy

A:

Q: en fr f(x) dx = √² Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then A True…

A:

Q: Which of the following is not true? Ⓒ √ 4dx √x(x+6) c lim dx ⒸS₁² 25² + x² ² m 25-x2 B dx c-5-0…

A:

Q: Iff is continuous on [a,b], then [xf(x) dx = x = xf²f(x) A True B) False f(x) dx

A: We will solve the problem

Q: 11.J sin 3 x sin 6 xdx 3

A: To evaluate the given integral.∫sin 3x sin 6x dx

Q: Suppose you are using a Leslie population growth model to study a species split into two age groups…

A:

Q: 22

A: We will solve the problem

Q: Given than an f* f (x) dx = -4 and Ⓒ ²1 (2) dua - [² 31 (2) dir = A f 3f dx 22 B [₁ f (x) da = 6 0…

A: We have to find the integral

Q: Scanned with CamScanner 10.f cota y sec y dy

A:

Q: please show step by step solution on how to get the circled part with complete explanation. do this…

A:

Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: As we know that; The trigonometric ratios;…

Q: Use parametric equations to describe the solution set of the line equation below. Give the exact…

A:

Q: Are you sure its correct? Because the formula for infinite sum is different

A: The summation of 2n-1/3n+2, n from 4 to infinity.