Find the area bounded by the parabola x = 8+2y-y², the y-axis, and the lines y = -1 and y = 3.

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

A: To find out the critical points of f.

Q: Which of the following is not true? A √ in(x²) dx = lim_ sin(x²) dx 3 3 dx dx Ⓒ 1² B In(x²) - = lim…

A: Solution is done in step 2

Q: x6 cos(x³) |dx=0

A: Follow the procedure given below.

Q: sin(x) L²₁(x² - 4x² + 3x)2 Jax-0 |dx=0 1 (1+x²)² (A) True B) False

A: We have to find the integral

Q: Which of the following is not true? ,5 @ 1²0x² 2 = m_ √ 25 - x² dx dx A o 25-x² lim c+5-0 ,3 ,3 dx…

A: We will solve the problem

Q: Trapezoidal method Quar x³dx for n=6 is equal to Blank 1 ("

A: Please refer to the image below

Q: 5 dx In evaluating 1 is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=5.91.…

A: ∫ 351x2-9dx

Q: Find the complete solution of ds dt = 5t* √√s.

A: Given problem:- Find the complete solution of dsdt = 5t4√s

Q: 2. Given f(x, y) = 12x2x³ + 3y² + 6xy. (i) Find critical points of f. (ii) Use the second derivative…

A:

Q: b iff and g are continuous on [a,b] and f(x) z g(x) for all x E[a,b], then f(x) dxz g

A: SOLUTION-

Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

A:

Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim 1-0…

A:

Q: Determine the values of a for which the system has no solutions, exactly one solution, or infinitely…

A:

Q: 4. fx√x - 3 dx

A:

Q: B.) For numbers 1 to 10: Determine if limit of each function exist using the piece-wise function…

A:

Q: 200 J + Corxiy_Tanx sinx dy

A:

Q: I. Find the sum of the following convergent series. lim = 348 lim lim 846 Σ [tan² (2n-1) - tan²¹…

A:

Q: 1. f(x + 2) ³dx A. (x + 2) + C A О в O 2. fe²x+1dx A. ²x+1+C O A. B. O C. B. 6(x + 2) + C B. e2x+1+C…

A: Here is the solution:

Q: Solve for x. O-1,-4 O -1,4 O 1,4 O 1,-4 x-1 3 2 x-2 =0

A: Given,      x-132x-2=0

Q: Q2. Find the exponential Fourier series for f(t): (1 = Fourier series. 0<t<1 (2 1<t<2 then find the…

A:

Q: Given the function y=f(x), y' is found to be positive over the interval (4,8), then over this…

A: if the first derivative of function is positive, then the function is increasing.

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: 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: C Let a and C be positive constants. Let be с the upper semicircle (x − a)² + y² = a² y ≥ 0, from…

A:

Q: Find f^-1(x) for f(x) = 9+8x f^-1(x) = ____

A: Topic = Function

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: Let's find absolute maximum and minimum value of given function.

Q: en fr f(x) dx = √² Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then A True…

A:

Q: Which of the following is not true? 5 dx dx (A) lim S o 25-x² c+5-0 25-x² 3 dx dx So in (x²) B √₁…

A: We have to determine integration

Q: dx 17.S (4x²-9)3/2

A:

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

A: Given problem:-

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

A:

Q: 11) Suppose that B, (fix) be the Bernsten polynomial. Then ((B₂B)(t.:x) = (b) x (c) x² (d) No Answer…

A:

Q: II. Solve the following problems: 1. A university holds an essay writing contest in English in which…

A: We have to find the winner essay.

Q: 2 a do (x + 2)²0 Using Simpson's method proper rounding off, no spaces) -dx for n=4 is equal to…

A:

Q: Find the indefinite integral: O x4+x+C Ox5/5+x²/2+c O x5 + x² + c O 5x5+2x²+c Sx(x³ + 1) dx

A: Given ∫x(x3+1) dxTo evaluate the integral:

Q: The population of a city is modeled by the equation P(t) = 357,512e0.25(t) where t is measured in…

A: We have to find how many years will it take for the population to reach one million.

Q: C.) For numbers 1 to 10: Determine if limit of each function exist using the graph below الات (-4,1)…

A:

Q: Are you sure its correct? Because the formula for infinite sum is different

A: The summation of 2n-1/3n+2, n from 4 to infinity.

Q: Which of the following is not true? 5 dx dx ® (Α Sº o 25-x² lim c+5-0 25-x² ® √ in(x²) dx = lim_…

A: We have determine the integration

Q: Find the complete solution of e sinx- - Note: fe" du = e" + C dy cos² x=0. dx

A: e-y sin x-dydx cos2 x=0⇒dydx cos2 x=e-y sin x⇒ey dy=sin x cos2 x dx⇒ey dy=sin x cos x·1 cos x dx⇒ey…

Q: y" + 5y' - 4y = 0

A: SOLUTION-

Q: Make Detailed solution INTEGRATION OF TRIGONOMETRIC FUNCTIONS

A:

Q: Calculate the effective interest rate for each of the following nominal interest rates: a. 3.25%…

A: This question can be solved using the concept of effective interest rate.

Q: A company produces computers. The demand equation for this computer is given by p(q) = -5q + 6500.…

A:

Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

A:

Q: This answer is incorrect do you know why?

A:

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, dv is set as: O ex dx O…

A: We have to find the dv

Q: Find the transition points. y = 2x6 =18x4

A:

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

A: Given f(x,y)=x2y3+3x3y∂f∂x=∂∂xx2y3+3x3y

Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. HI-4 (a) lim f(x)g(x) #114 (b) lim…

A: Given problem:-