Find the volume of the solid obtained by rotating the region bounded by y = −10+ 6x - x², x = 1 and x = 5 about the line y = 8.

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: 20

A: Please refer to the image below

Q: Suppose that fn ⇒ f on R and that each fn is a bounded function. Prove that f is bounded.

A: Solution

Q: In evaluating dx , is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=4.6. C-3+…

A:

Q: All continuous functions have antiderivatives. A True B) False

A: all continuous function have anti derivative.

Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: We have to find interest rate on the investment.

Q: Using Trapezoidal method √√x dx for n = 4 is equal to Blank 1 (use 2 decimal places with proper…

A: We need to use here, the trapezoidal rule.  ∫ydx = h/2 [ y0 + y4 + 2 ( y1 + y2 + y3 ) ]  For this…

Q: 4. 53-10x dx

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 1. fx³ In x dx

A: Evaluate the integral equation by integration by parts .

Q: Solve the differential equation: (1+x3)dy - x2ydx=0; y(1)=2

A: Solve the differential equation: (1+x3)dy - x2ydx=0; y(1)=2

Q: Using Simpson's method spaces) √²x² dx for n = 4 is equal to Blank 1 (use 2 decimal places with…

A:

Q: 6. Where does the normal line to the curve y = x - x² at the point (1, 0) intersect the curve a…

A: Topic = Functions

Q: All continuous functions have antiderivatives. (A) True (B) False

A: all continuous functions have antiderivative.  But noncontinous function doesn't have. It's true

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

A:

Q: 4. fx(1-x) dx

A: We can find the integration as below.

Q: Ive what is asked in the following problems. Write your solutions and box your final answer 1. Find…

A: Let's find tangent line and normal line equation.

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x- cos x (a) lim x/4…

A: According to the company rule we can answer only first question and rest can be reposted.

Q: Evaluate √x² + x + 2 dx x²-1 x+1 In: +C (x-1)² 0₁ (x-1)² In- + C x+1 O x + 1 (x-1)² (x-1)² x+1 X+…

A: Solution is here

Q: 4 35₂ In evaluating 2 dx X√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at x= 2.9.

Q: 9. f √x³-1dx x

A: Given: I=∫x3-1xdx    ...1 As we know that; ∫11+x2dx=tan-1x+C

Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: Ans=Trigonometric substitution  For detail...go through the solution....

Q: Iff is continuous on [a,b], and f(x) 20 then A True False ر VFX √f(x) dx = dx = √5 F(x f(x) dx

A:

Q: - y = sin² (3*)

A: We have to find derivative of given function.

Q: 3. f Arccos 2xdx

A:

Q: Show

A: Please refer to the image below

Q: If you evaluate the integral expression 12x-1|dx the result is Blank 1 (use fraction or decimal in 2…

A: Application of integration

Q: c) The equation of a straight line, of gradient m and intercept on the y-axis cis y = mx + c If a…

A: Let's solve.

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: Which of the following functions have a 4th derivative different from itself? 0x4 ex sin x COS X

A:

Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

A:

Q: dx 15. S (x²+36) ³/2

A:

Q: = Use the Riemann's Criterion for integrability to show that the function f(x) integrable on [0, b]…

A:

Q: 4. f(x) = 4x cosh 3x x² ; f'(2.7)

A:

Q: For the given function f(x,y)=x²y³+3x³y, find a flay O 2xy3+9x² y O 3x²y²+3x³ O 6xy²+9x² O 2+18xy

A: We have to define the derivative

Q: Convert the point with Cartesian coordinates 2 r and 0, with r> 0 and 0 ≤ 0 < 2π in radians. (r, 0)…

A: Topic = Geometry

Q: fx cos 2x dx

A: Let's solve given integration.

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

A: Given: Now, we find the mentioned ratios. sin A=662+102=6234=334cos A=1062+102=534tan A=610=35

Q: In evaluating 2 dx x√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if…

A:

Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: see below the answer and calculation

Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: If you evaluate the integral expression |2x - 3|dx the result is Blank 1 (use fraction or decimal in…

A:

Q: Using Simpson's method Blank 1 Add your answer √xdx for n=4 is equal to Blank 1 (use 2 decimal…

A:

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: We will find the solution.

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

A:

Q: dx 17. S√4e-2x-25

A: Given integral: ∫dx4e-2x-25.We need to evaluate the integral.

Q: 1² ax +6 cos(x³) (A) True B) False |dx=0

A: Here, x6cosx3 is an even function. So, ∫-11 x6cosx3dx≠0

Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x²x2 2…

A:

Q: Area A is bounded by the curves Y= X2 and Y=X2/2 + 2 a. Sketch area A and Determine the area of ​​A…

A: Let's solve for area and volume of given two curves.

Q: Find the area of the region bounded by the curves y=x4 andy=2x-x²

A:

Q: Given Cost and Price (demand) functions C(q) = 100q+40000 and p(q) = -2.7q+950, what profit can be…

A: We need to find profit.