12. The volume of a spherical cancerous tumour is given by the function V(r) = {ar³, where r is the radius of the tumour in centimetres. At the moment the radius is 1 cm, doctors estimate that the radius is growing at a rate of 0.8 cm/month. At what rate is the volume of the tumour growing at that time?

Q: 1. For the function g(t) whose graph is given below, state the value of each, if it exists. If it do...

A:

Q: 3- -3 -2 -1 1 2 3 Refer to the graph below to answer the following 5 questions. Record your answer t...

A: Part (a) As we see when x tends to -3, the left hand limit and the right hand limit of the function ...

Q: iv. An = In(n + In n

A:

Q: ii. 0.9,0.99,0.999, 0.9999,..

A: This can be written as  9/10, 99/100, 999/1000, 9999/10000..... (10-1)/10, (100-1)/100, (1000-1)/100...

Q: Find the parametric equations for the tangent line to the curve x=t^2−1,y=t^4+1,z=t^4 at the point (...

A: Given: x=t2-1, y=t4+1, z=t4 Point 8, 82, 81, is for t=3 as you can see substituting it in the three ...

Q: Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter...

A:

Q: DEvaluate the Riemann sum for f(x) = x- 1, -6<x<4, with five subintervals, taking the sample points ...

A: A function is given that is f(x) = x - 1. We have to find the Riemann sums for f(x) on the interval ...

Q: what is the derivative of y=e^-1/2x(C1cos3x+C2sin3x) and evaluate if x=0, y'=8

A:

Q: For the following exercises, use shells to find the volumes of the given solids. Note that the rotat...

A:

Q: if 2 and gcx) -X and h =1-2X %3D Find, fog fog, gof, gog, gofoh, fof > fof .

A:

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the ...

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: if y=6x^5, then dy/dx=

A: We know that; The Power law: ddxxn=nxn-1 And a.f'=a.f' Given: y=6x5

Q: Write down the first five terms of the following recursively defined sequence. a1 = -5; an+1= -2a, +...

A: Given sequence is  an+1=-2an+5with a1=-5To find the first five terms:  

Q: Q2: z = cos3xsin4y+2x²y az az azz a²z a2z Find : дх' ду' дх ду 'дхду

A: Given  z=cos3x sin4y+2x2y Differentiating partially with respect to x and y , we get ∂z∂x=(-3sin 3x)...

Q: Solve the differential equation (y /x² + y²) dx - xdy = 0. If y = 1 when x = /3, determine y whe +

A:

Q: Determine the Convergence Interval of the following series! (x – 3)" n² n=1

A:

Q: regions between the given curve and y= 1 ,y=1, and y=4 1+y 134 X= 2

A: Given: - The curve is, x=11+y2, y=1 and y=4 and y=0 around the x-axis. To find: -The volume generate...

Q: csc xcot x sin(csc x )dx

A: ∫cscx cotx sin(cscx) dx

Q: Find the smallest value of k e N for which the area under the graph of f(x) = x* + x between x = 0 a...

A:

Q: Variable Separable (6) (xy - 3y + x – 3)y' = xy + 2y – x - 2 (7) y' kM – ky; Provide the explicit so...

A:

Q: Find the partial fraction decomposition of the function. Write answer in simplest form. x² +x+1 a) f...

A:

Q: Question 2 In the expression /In²sinx -dx, the integrand is tanx Insinx A tanx B -Insin'x + C In sin...

A: Given:- ∫ln2sinxtanxdx To Find:- Integrand from given expression

Q: Show that In x lim x→1 x – 1 1.

A: To prove: limx→1 ln xx-1 =1 limx→1 ln xx-1 =00 form L'Hospital's Rule tells us that if we have an in...

Q: 1) appropriate (inverse) substitution, i.e. a correctly labeled right triangle: Reduce the following...

A: Since you have asked multiple questions, we will solve the first question for you. If you want any s...

Q: |The vector projection of v = 4î + 4j + 4k onto W = 5î - 4ĵ + 3k is aî + bî +cê: where the exact num...

A:

Q: 7. Find the x cand y nvercapts of f fG)=4hx" (x+7)3

A: Topic:- algebra  Note:- as per our guideline if more than one question uploaded than only first ques...

Q: Find the solution of the differential equation (x+ Vy² + 1)dx – (y - ху dy = 0 %3D Vy2+1,

A:

Q: If f(x) = In( 3 + e4x ), find f '(0). f '(0) =

A:

Q: (s+1 if s 1 (a) Find lim f (s) (b) Find lim f(s) S-1 s--1 2t +3 if t 1 2. g(t) = Find lim g(t) %3D ...

A:

Q: 1아 %3D %3D 3D -10 -15- lim_f(x) 2. lim f(x) x→-1+ 3. lim f(x) 1. x→-1- x→-1' 4. lim f(x) 5. lim f(x)...

A: Given problem:-

Q: 2n5-n2+4 i. an n²+1

A: Follow the procedure given below.

Q: Question Evaluate the integral below. dx

A: Given that: ∫x7e3x4dx

Q: Let   f(x, y) = √y - 2x.              NOTE: The y - 2x is all under the square root! - What is the...

A: As per the instruction, we will answer only the first one. Given f(x, y) = √y - 2x. So, domain for s...

Q: [tan*dog a) * dx x) x(1+log?: tan (log x) 8. 2

A:

Q: Find the ABSOLUTE VALUE of the gradients of the tangents drawn to the ellipse x^2/4+y^2/93D2 at the ...

A: We have to find absolute value of gradient at x=2 for the given function.

Q: Determine whether the following sequence is increasing, decreasing, or neither. 5n-2 i. an = 4n+1 ii...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: Evaluate the integral below along the given path. (Give your answer correct to 2 decimal places.) /(...

A:

Q: CAn equation of the plane through the point (2, 5, 7) that is parallel to the line 7 (t) = 3î + 2ĵ -...

A: Given problem:-  Find an equation of the plane through the point (2, 5, 7) that is parallel to the l...

Q: Question 1 A function F is an antiderivative of the function f on an interval I if for all x E1. A F...

A:

Q: Write an equation of the tangent line to the curve f (x) = 3/ Va + 8x at the point (4, f (4)). %3D U...

A:

Q: %3D cosx cotx sin x CSCX

A:

Q: Evaluate f 8e7x+e7= da

A:

Q: QUESTION 4 Given f(x) = 8x3 + 2x. Estimate the value of f(2.01) using differential.

A: Given that: f(x)=8x3+2x

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Q: Find the general solution of 4y'- 23y" - 33у" -17у — Зу 3D 0

A:

Q: The distance from the point (-1, -2, 3) to the line x = 1 + 2t, y = 2 - t, z = 3 - 2tis [a] (input e...

A:

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. ...

A: Given that: limn→∞nne-8n

Q: kf (x) dx =k ] f(x)dx Jas(a))dx=f (x) +C D

A:

Q: f(x)=2x^2+5x+3 find all values of x where the slope of the tangent line to is 0

A:

Q: Evaluate the integral. • T/4 sec*0 tan40 de

A: Given :