Consider the following initial-value problem. f'(x) = 6x2 – 8x, f(3) = 21 Integrate the function f'(x). (Use C for the constant of integration.) f'(x)dx = Find the value of C using the condition f(3) = 21. С 3 State the function f(x) found by solving the given initial-value problem. f(x) %D

Q: Determine the exact solution of the following differential equation y = 2 - y at y(0) =1. So the…

A: See this solution in below

Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0

A:

Q: The count in a bacteria culture was 600 after 20 minutes and 1500 after 35 minutes. Assuming the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 2. A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards…

A:

Q: x³ + x² - x - 1 lim X→1 X-1

A:

Q: a3z a3z 5. For z = x?siny show that дудхду ay²əx

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Convert to a polar 13. (0,-4)

A: Given, (x,y)=(0,-4)

Q: V1-x² dy dx |-V1-x²

A: Solution: ∫-11∫-1-x21-x2 1·dydx

Q: 18. Convert 5 radians into degrees. First find the exact answer (no decimals or rounding, please).…

A:

Q: equation of the tangent to the curve y = 1+ Int and x = t+ Int when t = 2

A: Topic:- application of derivatives

Q: Evaluate the following limits: x² - lim x→1 x-1 a) х-2 b) lim x→2 2- 16–x 2х -1 c) lim x→* x² +3x+5

A: a) limx→1x2-1x-1b) limx→2x-22-6-xc) limx→∞2x-1x2+3x+5

Q: Which of the following is the expanded form of E (-1)*(k+ 1)2? k=1 A -1+4-9+ 16 – 25 B -4+9- 16 +…

A:

Q: 2X + 2 ) dx 3. 2X 6 + 2e

A:

Q: nd 4 and using L'Hôpttal's Rule.

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, C = 6 (x – 6)²…

A: We have to find out the polynomial

Q: Find a vector that is perpendicular to the given vectors. 3) i = (-5, 6, 7) v = 1, -9, 0) 4) RS and…

A:

Q: Find the equation for the plane through the points Po(-5, - 2,- 2), Qo(3,2,4), and Ro(4, - 1,- 2).…

A:

Q: 1. Determine whether the series En=1 2n4+1 is convergent and explain why.

A: We have to find the convergent As per guideline we have to solve one question Please repost other…

Q: Question 3. Find f/ (x). If f(x) = tan-1x? %3D

A: we have to find out

Q: A ladder of length 8 meters leaning against a wall starts to slide. If its upper end slides down the…

A:

Q: dy 3. If y=u 3 and u = 4x2 - 2x + 5, give dx dy 4. If y=u? and u = x3 + 4 determine dx

A:

Q: 6. A particular leaf is comprised of 80 thousand cells. As the leaf grows, the number of cells grows…

A:

Q: False 1. If v, w, x E R" are vectors with v · w = 0 and w· x = 0, then v•x = 0 too. False 2. If v, w…

A:

Q: (-1)" Vn

A:

Q: 1. If sin 0 =, and 0 is in QI, find sec 0. 2. Given cos e = .e is in QIV, find csc 0. 3

A: We have to find out the trigonometric ratios

Q: Show that when a hole of radius a is bored through the center of the sphere of radius b, the volume…

A:

Q: Given the function h(x)=*-4 and k(x)=-+4. 9. 3 а) State the domain of h(x) and k(x). b) Find and…

A:

Q: 2. Find the general solution of cos x dy + (y sin x – 1) dx = 0 %3D

A:

Q: 4-2y -2 dx dzdy

A:

Q: Question Ris the region bounded by the functions f(x) = xr - 8x + 7 and g(x) = 5x- 33. Find the area…

A:

Q: rV1-y² (x² + y³) dy dx -1 J-V1-y

A:

Q: (b) Using logarithmic differentiation, find y if y =r' 5* cosh" 4r.

A:

Q: Question 9B.)

A: Topic:- function

Q: The function s(t) describes the motion of a partide along a line. s(t) = 12t – 2 (a) Find the…

A:

Q: incorrect The answer above is NOT correct. 1.8 F2 1,0 10 The slope of the tangent line of the…

A:

Q: tan e de gec e + 4 cose

A:

Q: If f(x) is an even function and f(x)dx = 5, find the value of , f(x)dx. %3D O 10 O 5 O cannot be…

A:

Q: Use the specified substitution to find or evaluate the Integral. (Use C for the constant of…

A:

Q: y = sinx from x=0 to x=n

A:

Q: Sketch the graph and show all extrema, inflection points, and asymptotes where applicable. 1) f(x) =…

A: Marked below in the graph

Q: Experimental data on the nitrogen content of soil samples taken from a field used for vegetation was…

A:

Q: Which of the following is a nonhomogeneous linear differential equation with constant coefficients?…

A:

Q: Find the first derivative of y = (x – 1) √ (2x – x2) + arcsin (x – 1) and y = arctan [ (3 sin x) /…

A: y=(x – 1)(2x – x2)   +sin-1(x – 1) y'(x)=d(x – 1)2x – x2   +sin-1(x – 1)dx        =d(x – 1)2x – x2…

Q: 2. a“y dx2 dy + 42+ 3y = sin(x) + 2 cos(x) dx

A:

Q: Evaluate the definite integral. es dx x/ln x v 5 6568542194924

A:

Q: 1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second…

A:

Q: ( 19 ' Evaluating cot 3 will yield to A 3 B -V3 D

A: Here, cot19π3cot6π+π3

Q: 2x²+x² x dx

A:

Q: Distinguish the Domain in A Function f of Two Variables from Range in A Function f of Two Variables

A: Suppose the function is: f:ℝ2→ℝ2

Q: 5. A small metal bar, whose initial temperature is 20°C, is dropped into a container of boiling…

A: According to newton law of cooling: dTdt=-k(T−Ta​)  Where T is the Temperature of the body and Ta is…