Problem 4. A rectangle is constructed with its base on the diameter of a semicircle with radius 5 and its other vertices on the semicircle. What are the dimensions of the rectangle with maximum area? Yo -4- X ·N -2 O -N-

Q: In evaluating 2dx E, is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x=1.13…

A: Integration

Q: Arrange the choices in order 1.2.3.. to prove: For any sets A, B and C A x (BUC) = (A x B) U (A x…

A: Here we have to arrange the option.

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

A:

Q: Show that for all n € N, one has 1 2√n+1 <√n+1-√n<; 2√ñ

A:

Q: | dx= - 3 J A) True B) False m|m

A: Topic = Integration FALSE

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

A: Please refer to the image below

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: What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan…

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: Derive the following function 1 1. v = x²√x + √²²³√x 2. g(r) = (r²2r)er

A:

Q: Solve the differential equation: (2x - 4y - 3)dy=(x-2y)dy

A:

Q: (-3)^(x-2)^. II. Consider the power series, √n+2 n=o 1. Use Limit Comparison Test to show that the…

A:

Q: For the function y =f(x), it was found out that f"(c) = 0. What can be said that x=c? critical point…

A:

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

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: Can you write it in a paper? I don't understand

A:

Q: R is the region bounded by the functions f(x) = -7 and g(x) = -4x - 10 over the interval [a, b]…

A: We have to find the integral

Q: Q:2. Use the first derivative test to find the intervals on which the function is f(x) = x4. which…

A:

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: 9.f tan3³ x √sec x dx

A:

Q: cos(x3 (A) True B) False dx=0

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

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

A:

Q: aces)

A: We will find the value of the integral

Q: in cacn case. Q2. Find the exponential Fourier series for f(t) = {2 Fourier series. 0 < t < 1 1 < t…

A:

Q: Find the derivative of sin In x O sin(Inx)/x O cos(Inx)/x O cos(1/x) O sin (1/x)

A:

Q: 22

A: We will solve the problem

Q: 3. Use Stokes' Theorem to evaluate $ F dr, where F = (0, 0, 2), (1, 0, 2), (1, 1, 2), and (0, 1, 2),…

A:

Q: In evaluating 5 dx =, is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=4.6.…

A:

Q: ог Question A.) Does this CONVERGE • DIVERGE ? (~) ² M nal

A: To determine whether the given series converges or diverges.∑n=1∞ln n2n

Q: 1²₁ (886x5)) dx = 0 cos(x3 A) True B) False

A: Answer is following.

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: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. Show solution and…

A:

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

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: A street light is at the top of a 18 ft tall pole. A woman 6 ft tall walks away from the pole with a…

A:

Q: 0,000? e marginal revenue is dollars per item. necessary, round to the nearest integer

A:

Q: * 5.8x √4x²+5 dx 2(4x²+5)³/2 A. +C 3 O A. OB. O C. * 6. f 35x-1 A. 35x-1 In 3 O A B 5x-1 dx C + C…

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: Find a particular solution of ds 1 π = cost determined by s=3 when t == = cos dt 3 ✓

A: Please see see below picture for detailed solution.

Q: 4. Find the area bounded by the given curves:y² = x + 4, x - 2y + 1 = 0

A: Answer is given in next step.

Q: Find the length of the arc of a circle of diameter 10meters subtended by a central angle of π/4…

A: Given:  diameter =10meters

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

A:

Q: • Find the sum of the following convergent series. lim lim lim tan ¹ (2n+ 1) - 346 11 11 11 [tan…

A: Given problem:-

Q: Iff is continuous on [a,b], then [xf(x) dx = x = xf²f(x) A True B) False f(x) dx

A: We will solve the problem

Q: y = log₂ (1+x²)

A:

Q: 3.§ sin* 2 x sin 4 xdx

A:

Q: [²(x². x7-4x⁹+ (A) True B) False sin(x) (1+x²)² dx=0

A: We have to find the 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: ex = cosy

A:

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

A: