A) Link between plane and line in the differentiation. 7) Find the aquations of alono pocinh the point (54) m

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

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

Q: please show step by step solution on how to get the circled part with complete explanation

A: The given integral:∫x2+2x-2x2-2x+2dx

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: 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. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: 5. sin(x + y) = y² cosx

A:

Q: ow that the differential form in the integral below is exact. Then evaluate the integral. 5,1) 20x…

A: We have to examine that the given differential form of intregal is exact or not .after that we have…

Q: 8. f₁(r + 1)²dr Hint: square first

A:

Q: - 2500q, what cost is incurred when marginal profit is $0? Given Cost and Revenue functions C(q)…

A: In this question, we need to find the cost when the marginal profit is $0.

Q: Find the area of the surface obtained by rotating the line y = 19x + 6 about the x - axis from the…

A: Area of surface is evaluated.

Q: Question A.) Does this CONVERGE or DIVERGE? er 2 (lan) ² W nal

A:

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

A: Follow the procedure given below.

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

A:

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

A:

Q: Find the length of the arc of a circle of diameter 1010 meters subtended by a central angle of π4π4…

A: Solution ) diameter - 1010 m , angle = π/4 Radius =  1010/2           = 505 m length of arc of…

Q: y = ln √4x² (Hint: Apply first a property of LOG.)

A: Let's find first derivative.

Q: Q2: Find Maclaurin series for the function f(x) = (4-x) (four terms only), then find the error…

A:

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

A: The Simpson's 1/3 rule for integration is given by, ∫ab f(x)dx≈Δx3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+…

Q: Find the determinant of the matrix, O22-122-13 O22-12A +13 O²+12+13 02-13 2-11 4 6 2-1

A: Topic = Determinant

Q: iii. lim (1-sin x) tan x x→ I COS cos((x - 1)) iv. lim I-0 r³3r

A:

Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

A:

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

A: We have to solve the integral

Q: Question 11 Find the determinant of the matrix, A 2-13 B 2²-12λ + 13 C 22-122-13 D 2²+12+13 2-11 4 ]…

A:

Q: Find the line integral along the given path C. f(x - y)dx, where C: x=t, y = 5t+7, for 0 st≤5 C √(x…

A: Topic:- application of integration

Q: dy dt when x = 2. Let xy = 3 and Find dx dt 5.

A:

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: Find the line integrals of F = 4yi + xj + zk from (0,0,0) to (1,1,1) over each of the following…

A:

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: Find the slope of the tangent line to r²e³ + y²e² = 2e at (1,1).

A:

Q: 2 [² fo Given f(x,y) = x²y-3xy³. Evaluate fdy

A:

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

A: SOLUTION-

Q: s={ 3112 4'2'3'9' =(5, 5.5, 6, 6.5, 7, 7.5,...} = {√2,2√2,3√2, 4√2,...} ={√2,2,2√2,4,...}

A: Topic:- sequence and series

Q: Consider the diagram shown below. Suppose that O = (0,0) and A = (3.2, 0) and B = (2.71, 1.7). The…

A:

Q: A tumor is injected with 0.820.82 grams of Iodine-125. After 1 day, the amount of Iodine-125 has…

A: I have appended the formula used in the solution part of the question

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 3), and (2, 0).…

A: SOLUTION-

Q: 5. fe²x sin x dx 2x

A: Given ∫e2x sinx dxTo evaluate the integral:

Q: 2. f(x) = 3x4 +√4x; f" (1.2) 6

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: Question 32 What integration technique can be used to integrate: A Trigonometric Substitution B)…

A:

Q: Draw a picture to find ALL angles in 0 ≤ 0 < 2TT. 1 Ay mple: For tan(0) = = draw a circle. Label the…

A: Topic :-  trigonometry

Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

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: Suppose a population of fruit flies changes at a rate of g(t) = -3e0.01, in flies per day. If the…

A:

Q: 1 2 3 4 5 ements below that you agree with. be checking more than one box. No partial credit.…

A: Topic:- calculus

Q: = - - 6q² + 700q, where R(q) is in dollars and q Suppose a product's revenue function is given by…

A: The revenue function is given by , R(q) = -6q2+700q

Q: Consider the function f(x) exact values. f'(x) = f''(x) = f'''(x) = = Compute each of the following.…

A: Topic:- derivatives

Q: da potential function f for the field F. F = (4y + 2z)i + (4x+z)j + (2x+y)k eneral expression for…

A: Topic:- application of integration

Q: g(x) = 3 ln(x - 2)

A: