2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

Q: For the function whose graph is shown below, at which value of x is the graph continuous and…

A: We know  Function differentiable if it is continuous through out its domain   At sharp/corner points…

Q: 3. A right circular cone has the following dimensions: Radius: R Height: H Then its volume is R²H.…

A:

Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: 10- There is a rectangular playing field in Alaska Denali Park for a grizzly Bear with an area of…

A:

Q: Prove the limit below exists and find its value to 6 digits but replacing n for a large value and…

A:

Q: Convert the angle 270° to radians. Give the exact value and use pi for .

A:

Q: Vertex: Axis of symmetry: X f(x) = −(x + 1)² + 2 -10 -8 -6 -4 -2 10- 8- 6- 4 2- -2- -4- -6 -8- F~ 2…

A: Concept: Vertex: on the parabola, the greatest and lowest pointsAxis of symmetry: It's the straight…

Q: Prove the limit below exists and find its value to 6 digits but replacing n for a large value and…

A:

Q: c) What is the loss the company incurs when it tries to maximize sales (that is, produce the maximum…

A: Find out the loss the company when it tries to maximize the sales.

Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A: Recall:  V=∫abπf(x)2dx We have a=0, b=6, f(x)=e-x

Q: Find the critical values (if any) of the given functions. With solution please.

A:

Q: Researchers fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in…

A:

Q: State the order of the given ordinary differential equation. (1-x)y" - 9xy' + 6y = cos x 2 Determine…

A: We need to find order of D.E.

Q: 19. Find x from the following equations: 27x = 9y 81*3-* = 243 A. 2.5 B. 2 C. 1 D. 1.5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: dy 1+x²)²e³ = -2x dx

A: Topic:- differential equations

Q: g(x)=x5bx³ +a+c. Use calculus to: St (a) Find the critical points of g(x). (Round the y-value to 3…

A: Given a=15, b=12 & c= 15

Q: Find the area of the region enclosed by the curves y=2 sin x y = 2 sin x and y=2 sin 2x for 0≤x≤ T.…

A:

Q: Suppose f(-1) = 1, f'(-1) = 5, and g(x) = x³ f(x). The tangent line to g(x) at x = 1 is given by y =

A: The objective is to find the equation of tangent line .

Q: 2. Consider the function F, that assigns x in its domain to x²-1 F(x) = |x-1| In its domain. a. What…

A:

Q: 3 E (It=X) xp x te

A:

Q: 3. Evaluate III 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octant.

A: Use triple integral

Q: 2. Evaluate: Lel el-1 dx

A: 2.The given integral,∫-12ex-1dx

Q: 2x³ − 45x² + 300x + 6 has one The function f(x) = 2x³ local minimum and one local maximum. This…

A: Given: Axis interception points of 2x3-45x2+300x+6:  X Intercepts: -0.01994…, 0, Y Intercepts: 0,…

Q: Write the product as a sum or difference: 20 cos(482) sin(162) =

A:

Q: • III.6 622 dV where G is bounded by r + 2y +4:= 8 in the first octant. 3. Evaluate

A:

Q: Find the area of the region enclosed by the curve y=x²-3x³ + 2x² at interval from x=0 to x = 2.…

A: The graph of the curve y=x4-3x3+2x2 is To evaluate: The area of the region enclosed by the given…

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

A:

Q: integrate [(x csc^2 (2x) - x cos (2x)] dx

A: Given problem:-  ∫ [(x csc2(2x) - xcos(2x)] dx

Q: (b) [x² x²9x8 – 12x4 + 4 dx 2

A: We need to solve integral.

Q: Determine if the function f(x) is continuous and/or differentiable at x = 5? x+5 for -5≤x≤5 f(x)= 2x…

A:

Q: Betermine the value of k for which the following planes are perpendicular: π₁ = (1, 2,7) + s(4,2,0)…

A: π1 = (1,2,7)+s(4,2,0)+t(k,1,2)  First need to find the normal of the planeIf the plane in the form…

Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A:

Q: 1. f(x) = 4x² (8x + 1) 2. f(x) = (100x² + 25x)(10x² − 15x) 3. f(x) = (2x + 1)(4x + 3) (5x - 1)

A: Let's solve all given derivative by using product rule.

Q: 2 z² +4 lim z 2i 2z²+(3-4i)z-6i

A:

Q: dx f(x2²x+10) ² २

A:

Q: The function f(x) 2x³ + 42x² = one local minimum and one local maximum. This function has a local…

A: You must have an idea how to use derivatives to find the local maximum and minimum using critical…

Q: Evaluate: lim 1+ O 1 a 00 none of the choices In aª (A)

A:

Q: Find F(s). ℒ{et sin 3t}

A:

Q: Find the acceleration u= 2x² + 3y, v=- - 2xy + 3y² + 3zy, Example the following flow field: W =- at…

A:

Q: Differentiate the function with respect to the independent variable. f(x)=-7x+5x³-6 f(x) =

A: Given, f(x)=-7x4+5x3-6

Q: 4. Let v = (v1, v2, v3), w = (wi, w2, w3) be two non-zero vectors not on the same line in R Suppose…

A: answer is in next step. please give a like !!!

Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (8y² − x² + 7) dy = 0 s exact. If…

A: Topic:- differential equations

Q: en the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q² − 2Q³…

A:

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does…

A:

Q: Consider the following. √u-5(6 - ² + ¹0) du Simplify the integrand by distributing u-5 to each term.…

A:

Q: f(x)=0.2+25x-200x² +675x³-900x¹ +400x³ a=0 ve b=0.8 a.) find the integral by using Simpson 3/8 Rule…

A: Concept: Simpson's rule: One of the numerical approaches for evaluating the definite integral is…

Q: Find the area of the region enclosed by the curve y=x²-3x³ + 2x² at interval from x=0 to x = 2. y…

A:

Q: Find the area moment of inertia with respect to x of the plane region y=9-x^2 bounded by the…

A:

Q: Write the equation of the circle centered at (1, 10) with radius 3.

A: