A population numbers 20,000 organisms initially and grows by 15.1% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = ab', where P =

Q: A dancing contest has 11 competitors, of whom three are Americans, two are Mexicans, three are Russi...

A:

Q: tan(tan3x)dx Evaluate: cos-3x -In |sec (tan3x)| + C (B ® - in [cos(tan3x)| + C © - sin( tan3x)| + c ...

A: We need to evaluate the following integral I = ∫tantan3xcos23xdx                            ...........

Q: If f(x) = a +2a + 4, then the estimation of the area under the curve y = f(x) between 1 <r < 2 with ...

A: We have to choose correct option

Q: 4" – 3" 00 Determine whether the series converges or diverges. If it converges, find its sum. n= 0

A: Solution: ∑n=0∞4n-3n5n Apply series ratio test an+1an=4n+1-3n+15n+14n-3n5n

Q: et kdt k A True B) False

A: First we solve L.H.S then solve R.H.S . We use the formula integration of eat=eat/a

Q: Suppose f'(x) is continuous over an interval a < a < b, and a <c <d < b. If f'(c) = 9, then (check a...

A:

Q: Let m and n be positive integers and a+ 0. Using partial integrals, show that 1 x"ea# dx = -x"eª* n ...

A:

Q: What is the value of f(x)dx; if ca+1 2 S* f(x)dx = ?

A: Integration

Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2. Sh...

A:

Q: 1- arctan x dx

A:

Q: Determne whether the hamit exitis or not when a)x3 and b) x→ -3 x²-9 when x< -3 F(x)= 9-x² when -3< ...

A: Limit exists if, LHL = RHL Limit does not exist if, LHL≠RHL

Q: Exercise 7. GREEN'S THEOREM Use Green's theorem to calculate fo F R. All curves are oriented counter...

A:

Q: Evaluate the integral, then find 1- 3a. w – 1 dw - = w + a ln (w+ 1) + C w + 1

A:

Q: x-'In²(Ine*) dx A Inx B Inx C Ine" D Inx2 E) None

A:

Q: The function f(x) = 2a – 392? + 240x – 4 has two critical numbers. The smaller one is x = and the la...

A:

Q: Find the absolute maxima and minima of the function on the given domain. T(x.y) =x +xy+y- 12x+2 on t...

A: Given

Q: Let s(t) = 6t – 27t² – 180t be the equation of motion for a particle. Find a function for the veloci...

A: We need to find velocity and acceleration function.

Q: Calculate the divergence of the vector field F (x, y, z) = –10 sin(2xy)i – cos(x'y)j. (Give an exact...

A:

Q: 2 Find all local extreme values of f(x) = a 3 5x2 + 8x – 50. The FIRST local extreme value, moving f...

A: topic- application of derivatives

Q: 1 4lnr Evaluate: | (A +C - 2(r5 – 3) +C 2(,5 – 3) 2 +C 15 4lnr 4

A:

Q: Find the area of the region enclosed by the curves  f (x)  =  4x + 15 and g(x)  =  2x + 33, and the ...

A:

Q: The Taylor polynomial of order 2 generated by a twice-differentiable function f(x) at x= a is called...

A:

Q: Evaluate: thr (,5_ 3) ² dr A 2(r-3) 3 B +C 3 2(,5– 3) ? +C 15 4nr D 4.

A: This question is based on Indefinite Integral.

Q: Classes Canva Notion - The all-i. Instagram (5) Home / Twitter A Facebook YouTube l Bea Elaisa Alvar...

A: End behavior of given polynomial is if x tends to ➕➖ infinity♾️ then f(x) tends to infinity. 

Q: Differentiate the functions. a) f(x) = 1 – 6x +x7 b) f(x) = (x³ + 3)² %3D

A: a)f(x)=1-6x+27x7Differentiate with respect to x   f'(x)=-6+(27×7x6)  f'(x)=-6+2x6Derivative of f(x)=...

Q: Find the slope of the tangent line to the curve 3z? – 2xy – 3y3 = 63 at the point (3, – 2).

A: topic - slope of tangent line to curve

Q: (х +у—4)dx — (х — у + 2)dy %3D0 -

A:

Q: QI/Correct the following items, enhance your answer with a mathematical proof for each item. 1- cosh...

A:

Q: - In²(Ine*) dx A In²x B B Inr Ine D Inx2 E) None

A: topic - definite integral

Q: -7. -5-4 -3-2 -1 \I 2 3 4 5 -2 -4- o ト oゆ!

A:

Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

A:

Q: Express the integrand as a sum of partial fractions and evaluate the integral. (Hint: factor the den...

A: Given, Evaluate ∫5x2+x+36x3+9xdx

Q: x + 3x + 4x + 1 dr (x2 + 2x + 2)²

A: Given ∫x3+3x2+4x+1(x2+2x+2)2dxPerform partial fraction decomposition=∫x+1x2+2x+2dx-∫1x2+2x+2dxNow so...

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Here, the given curve bounded by : y=x-1, y=0 &amp; x=6       

Q: For the equation, find  dy/dx  evaluated at the given values. y2 = 2x − 13  at  x = 7, y = −1 dy d...

A:

Q: :-'In²(Ine*)dx A In?x В Inx C Ine* D) Inx2 E None

A:

Q: Question Select multiple answers and then press Answer. p(x), r b f(x) is continuous on (-00, a) and...

A:

Q: Given the differential equation y" + 7y' + 12y = 8x e-3x Determine the General Particular Solution f...

A:

Q: 2. Stanley Ford makes mountains out of molehills. He can do this with almost no effort, so for the p...

A:

Q: A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec. How fa...

A: Given; A balloon leaving the ground 60 ft from an observer rises vertically at the rate of 10ft/sec.

Q: At an exhibition, the probability of visitors on the first day is 3/5. The ticket price for a visito...

A:

Q: S e3(2e * – 1 ) dx (ear – 2) (e3* + 1) 4 (A) 2e3x – 1 B) 2e 6r – e 3x © (e3r – 2)+ D (e*+1)+ (E ,6x ...

A:

Q: Compute T2(x) at x = 1 for y = eª and use a calculator to compute the error |e – T2(x)| at x = -1.5....

A:

Q: Find the arc length of the curve x -3y3/2 from y = 0 to y = 10. Length

A: Integration √1+(f'(y)) 2dy

Q: 6t dt = 3a? %3D Select one: O True O False

A: topic - definite integral

Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: Question / Iil Use the defination of improper integray to define 1. dox 1.2 use your defination in H...

A:

Q: Consider the series (9x). n=0 (a) Find the series' radius and interval of convergence. (b) For what ...

A:

Q: 3. Construct an angle of 65° from two straight lines and bisect the angle.

A: Construct an angle of 65 measure at O using protractor

Q: Choose x such that the following two vectors are parallel u = (-5, 7, – 9) and v = (25, x, 45)> -7 N...

A: