Let f(x, y) = x(y - 3) and F = Vf. If r =< 3-1², 2-t> with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c. 11 d. O e. 7 None of these

Q: Power series 2. √n+2 n=o Limit Comparison Test to show that the se=

A: Given is       power series ∑n=0∞(-3)n(x-2)n(n+2)when x=53∑n=0∞(-3)n(x-2)n(n+2)=…

Q: rk the critical points on the following graph. z2 - 14 70 56 42 28 14 3 4 5 " -4 -3 -2 -1 -14 -28…

A: Topic:- calculus

Q: The current population of a certain bacteria is 2849 organisms. It is believed that bacteria's…

A:

Q: Find the augmented matrix for the following system of linear equations. 6x₁ + 8x3 = -8 5x₁7x2 + x3 =…

A: Given system, 6x1+8x3= -8 5x1-7x2+x3= -3 9x1+8x2-3x3=7

Q: f sin-¹(x) dx

A:

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: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: Suppose that ƒ is continuous and F(x) = g> 0, g'>0 and integrable on [a, b) and that lim g(x) = I-b-…

A:

Q: - y = sin² (3*)

A: We have to find derivative of given function.

Q: 100 Ln=1 a. Converge 3 b. C. d. Diverge (-3)2+1 is 23n 318 338 8 b 2 2 0 J d a *

A: The objective is to check the convergence or divergence of the series.

Q: Evaluate the following definite integral using substitution rule. 1. (2x - 1)² dx 2. fx √x² + 1 dx

A:

Q: Derive the following function 3. y=x√x 4. y = ³√x + ³√x

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: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

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

A:

Q: Iff is continuous on [a,b], then rtf(x) dx = π f(x) dx 1 A True B) False

A:

Q: d²y dy 4. (a) Compute the general solution for: +4 dt +3y=e-t/2. dt² (b) Compute the solution with…

A:

Q: Use the given information to find f '(2). g(2) = 3 and g'(2) = -2 h(2) = -1 and h'(2) = 5 g(x) h(x)…

A: Given, g(2)=3 , g'(2)=-2, h(2)=-1 , h'(2)=5, f(x)=g(x)h(x)

Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A:

Q: Question 2 Iff and g are continuous on [a,b], then t True B) False in √ [f(x)g(x)]dx = {√°f(x)dx)(√°…

A: Given that f and g are continuous function on [a,b].

Q: dx 17.S (4x²-9)3/2

A:

Q: Find the transition points. y = 2x6 =18x4 (Use symbolic notation and fractions where needed. Give…

A:

Q: Evaluate the definite integral number 3 using substitution

A:

Q: 5.12 7 ln 3x dx X

A: Is multiple questions are posted we are allowed to solve only 1st question...so please upload again…

Q: Determine whether there exists a function f : [0, 2] → R or none such that f(0) = -1, f(2)= 4 and…

A: In this question, we need to determine whether there exists any function for the given conditions.

Q: Which of the following is not true? ,5 Ⓒ √√² 25²x x² = 11m -√² 25-4x2² dx dx A lim o c+5-0 3 3 dx dx…

A: We have to find out the option

Q: Proving by Mathematical Induction A. 1. If P(2) = 1·3+2+4= 2(3) (11) 6 2. Prove that P(n) is true…

A:

Q: (2) Solve for all values of x over the interval [0,27]: 2sin(x) = sin(2x)

A: Topic = Trigonometry

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.

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: 4: Find aun -2 2y² Sin(xy) dx dy

A: Topic:- application of integration

Q: D. Diego walks at the rate of 5 ft per second toward a street light whose lamp is 20 ft above the…

A:

Q: Given f(x,y) = x²y-3xy³. Evaluate 2 S₁² 0 fdx

A: Follow the procedure given below.

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

A: using the simpson's method ∫01xdx for n=4.

Q: 까지 dx 10. A. In x + C B. In² [x] + C C. m² 1x1 xl 2 + + C

A:

Q: dx 20.5 x√4x²-49

A:

Q: In evaluating x=3.98. dx x²-9 is same as evaluating lim (In(f(x))). Determine the value of f(x) if…

A: First we evaluate f(x) using substitution

Q: In evaluating Add your answer 2 dx is same as evaluating lim cos-¹(f(x)). Determine the value of…

A: Given problem:-

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

A: Answer is given in next step.

Q: 5. Find the equation of the tangent lines to the curve y = x² + 3x -4 and parallel to the line 6x…

A:

Q: 2 ist dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding off, no Jo (x + 2)²…

A: Given,  ∫012x+22dx ,  n=4

Q: Scanned with CamScanner 10.f cota y sec y dy

A:

Q: Using Simpson's method √x³dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding…

A:

Q: f(x) = x - 52¹/5 (A) Find all critical values of f. If there are no critical values, enter -1000. If…

A: Since you have posted multipart questions i can do (A-E) covering three subparts critical values,…

Q: S= x² +2 (x-2)(x²-2x+2) dx U 2-2x 3 (√(√² ²²2²X + 2 + x ²³ 2₂ ) dx X-2 2-2x

A: given ∫x2+2x-2x2-2x+2dx

Q: Find the indefinite integral: 10sin 3x - 15 cos 2x + 6 e5x + C O 90sin 3x -60 cos 2x + 150 e5x + C…

A: 30∫cos3x+sin2x+e5xdx=30· ∫cos3xdx+∫sin2xdx+∫ e5xdx=30·…

Q: ,1 x² - 4x⁹+ A) True B False sin(x) (1+x²)² |dx=0

A:

Q: 18. f (x+9)dx x²+6x+25

A:

Q: Using Trapezoidal method 3 x³dx for n=6 is equal to Blank 1 (use 2 decimal places with proper…

A: Let's solve given integral by using trapazoidal rule.

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