Find the volume of the solid obtained by rotating the region bounded by y = 6x + 30, y = 0, x = 0 about the y-axis.

Q: Find the area of the shaded region. f(x) = -x³ + x² + 16x 3) g(x) = 4x (-3,-12) 30+ 20 10- -20- -30-…

A: Given curves equations:- fx=-x3+x2+16x , gx=4x

Q: Given: triangle ABC, find the length of side b. Round to the nearest integer. A. 110 ITF B. 111 A…

A: We are required to find the length of side b using the data given in the figure.   In ∆ABCLength of…

Q: -16 f(x) = 3x² + 4 -12 -8 f(x) -4 -8 0 f'(x) 4 Predict #3 8 If we changed the 3 to a −3 in the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: For 3 and 4, a and b are constants (with a, b nonzero in 4). Your answers should involve a and/or b,…

A: According to the bartleby guidelines we supposed to do the first one of multiple questions  kindly…

Q: Find lim f(x) if, for all x > 1, x →∞ 12ex - 21 4ex < f(x) < 3√x VX-1

A:

Q: 14 cout 5. + 3+ 2 2 -2+ -3- ress play to show imation Watch the values of f(x) as the x value…

A: To determine what y‐value is fx getting closer to as x approaches 1 from the right side.

Q: Write out the form of the partial fraction decomposition of the function (See Example). Do not…

A:

Q: Find the standard equation of the parabola which satisfies the given conditions. vertex (7,11),…

A: Given:- vertex7,11 and focus 16,11

Q: Solve the separable differential equation dy t dt t²y+y Use the following initial condition: y(0) =…

A:

Q: Find each x-value at which fis discontinuous and for each x-value, determine whether f is continuous…

A:

Q: how long will it take for the population to reach 140 grams

A:

Q: 11. f(x)=x²+x; x = 0

A: Asked question 11) f( x ) = x2 + x

Q: 2 (xy + x)dx = (x²y² + x² + y² +1)dy

A: Given differential equation ( xy + x )dx = ( x2y2 + x2 + y2 + 1 )dy

Q: Find the limit lim (x,y) →(15,3) xy cos(x - 5y)

A: The limit is given by limx, y→15, 3xycosx-5y To evaluate: The value of the limit.

Q: Find the rectangular coordinates of the point whose spherical coordinates are given. (a) (3, 0, π/2)…

A: Here is the solution:

Q: Find the area of the region that lies inside both curves. r = 4 + cos(?),    r = 4 − cos(?)

A:

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

A:

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: (1+t)²-1 t b. lim. t-0 =(t+1)

A: Topic - Limits We are given b.)limt→0(1+t)2-1twe know that(a+b)2=a2+b2+2ab

Q: 2. A portion of the graph of the function y = f(x) is shown in the figure. (a) State the domain and…

A: By the authoring guidelines of Bartleby, we can answer only first question from multiple question.

Q: 4. lim_ x² (1 - e¹/²) using l'hopital

A:

Q: What is the second derivative of the graph below at x = 1? -5 -4 -3 -2 f "(1) = 5 4 3 2 da 4 I 4

A:

Q: For the position function s(t)= - 16t² + 110t, complete the table shown below with the appropriate…

A: Let's fill the given table and find instantaneous velocity at t=4.

Q: 38. lim (√9x³ + x - x³/2) x →∞

A: given that limx→∞9x3+x-x3/2

Q: The vector v = ai + bj is perpendicular to the line ax + by = c. Use this fact to find an equation…

A: Given that , Vector : v=3i^+7j^ Find the equation of line through point P7,3 perpendicular to v.

Q: F(x) = 5x²-x+2 f(a+i)=

A:

Q: Evaluate the limit t³ - 1 1 lim t 1 ²

A:

Q: If we changed the 4 to a 3 in the equation of f(x), what would happen to the graph of the…

A:

Q: n x + 3xn-kyk +yn 2 x² - y²

A: Given: fx,y=xn+3xn-kyk+ynx2-y2 To find: whether the function is homogeneous or not, if yes find the…

Q: a) Find the simplified form of the difference quotient for the function f(x) = 5x²-x. b) Complete…

A:

Q: QUESTION 5 a) Use Divergence Theorem to evaluate the flux ff Fonds F(x,y,z)=+zk and S is the surface…

A: A detailed solution is given below.

Q: y = f(x) 10 Answer: 2947654321 6 -9-8-7-6-5-4-3-2-₁ ISPRS 7 -8 -9 -10 Evaluate: g(f(9)) 1 2 3 4 5 6…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) I = (x+27)/X^2 +24x +148 dx

A:

Q: ind the largest interval which includes x = 0 for which the given initial-value problem has a unique…

A:

Q: For the position function s(t)= - 16t+111t, complete the following table with the appropriate…

A: Given: s(t)=-16t2+111t Time interval [1,2] [1,1.5] [1,1.1] [1,1.01] [1,1.001] Average…

Q: Use sigma notation to write the sum. [s - (‡)] + [∞ - (3) ] + … + [s - (3-)] 6

A:

Q: incorrect

A:

Q: Determine the slope of the tangent line, then find the equation of the tangent line at the given…

A: We have given parametric equations x=6t y=3t3 When t=-1 x=6-1=-6 y=3-13=-3 Say,  x1,y1=-6,-3…

Q: A Linear Programming Problem with two variables 1. Minimize g =12x+8y subject to x + 2y ≥10 2x+y 211…

A: A detailed solution is given below.

Q: sin ln x X dx = (

A: formula used is d dx(lnx)=1x∫sinxdx=-cosx+c

Q: Find the distance from the point P to the given line L. P(0, -1, 2) and L: x=2 + 3t, y=-3-2t, z = -3…

A:

Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A:

Q: Compute the area of the parallelogram with vertices A(2 1), B(5,0), -2) and D(4, -1).

A: We are asked to find the area of the parallelogram

Q: Estimate using the linear approximation equation the value of 2023.

A:

Q: Use sigma notation to write the sum. 22 [(²-) - ²] (²) + ··· + [(²²) * - ²](²) [(7)-(%) 1 Σ

A: A detailed solution is given below,

Q: Find the exact value of the expression, be sure to justify your answers. tan sin -¹ (/)

A: Given

Q: Use the graph to find the following limits and function value. a. lim f(x) X→2 b. lim f(x) x→2* c.…

A: Topic - Limits We are given a graph of a function.

Q: Find the volume of the solid obtained by rotating the region bounded by about the line y = 8 y = x¹,…

A:

Q: Find the volume of the following solids. The base of a solid is the region between the curve y =…

A: Given:the base of the solid is the region between the curve y=2sinx and theinterval 0,π.

Q: 1 7. For f(x) write the linear approximation at a = 0 and estimate f(-0.1). (Note: The derivative of…

A: Let's find value of f(-0.1).