Determine the exact solutions to cos: O ○ 0=160=² ○ 0-5,0- 7x 0= 6 6 O O 0 7x 6 5x 6 R 0= =,0= 6 11x 6 117 6 √3 2

Q: Solve: dz + 4x = yº O 11r¹y+y¹¹ = C O 1lry - y¹¹ = C O 11xy + y = C O 11x¹y - y¹ = C

A:

Q: Sketch the region enclosed by y = 5x and y = 6x². Find the area of the region.

A:

Q: Find the area under the curve y=sin2xcosx for the given limits; sketch the area. Hint: integral in a…

A: Topic:- application of integration

Q: Use series to evaluate lim X→0 ex-(1+x) 4x² lim X→0 (Type a simplified fraction.) ex-(1+x) 2 4x²

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) 7 y = 6√x + 7 x dy = (3x72xx)dx…

A:

Q: c) 2 √9x²-16 x² dx

A: Given problem:- ∫9x2-16x2dx

Q: 5x9 8. What are the restrictions on the variable for · 2 x + 13x + 42 a) x # 6, x # 7 b) x −6, x‡ -7…

A:

Q: Consider the function f(x) = 1-5x², -4≤ x ≤ 1. The absolute maximum value is and this occurs at x =…

A: Consider the function fx=1-5x2, -4≤x≤1.To determine absolute maximum and absolute minimum value of…

Q: Set up the definite integral required to find the area of the region between the graph of y = 17 -…

A:

Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

Q: Let f(x) x³ + 6x² 36x +11. = (a) Use the definition of a derivative or the derivative rules to find…

A:

Q: The position function of an object is given by r(t) = (t2, 8t, t²- 28t). At what time is the speed a…

A:

Q: Consider the following second-order differential equation with constant coefficients, d² - z (x) − 8…

A:

Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

A:

Q: 6. Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

A:

Q: 5. Find using first principles the slope of the tangent to f(x) = x² + 6x + 9 at x = -3.

A:

Q: A1. SOLVE STEP BY STEP IN DIGITAL FORMAT Using the following function and the given intervals…

A: Given - f(x) = 4x^2 - 6                [ 3 , 6 ] ∆y/∆t =[ f(X2) - f(X1) ] / ( x2 - X1)

Q: Find the distance from the point A to the line through points B and C. Then show that the triangle…

A:

Q: Find the radius of convergence, R, of the series. R = 00 I = n = 1 xn n45n Find the interval, I, of…

A:

Q: Let f(x) = x¹ - 50x² 3 (a) Use the definition of a derivative or the derivative rules to find ƒ'(x)…

A: "since you have posted a question with multiple subparts,we will solve first three subparts for…

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A: Here is the solution:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: Find the shortest distance r1 between the two lines given by r₁ (t) = (3 + t, 3t, 5 – 4t) and r₂ (t)…

A:

Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

A:

Q: 8. Find the equation of the exponential function g(x). (No Decimals) Equation: -6 a

A: Solution ) from the graph  ( 0 , - 2) and ( 1 , 2 ) points are on the graph  Equation of exponential…

Q: 2 8. y' + ²y = -x²y² cos x

A:

Q: Evaluate the definite Integral. Use a graphing utility to verify your result. [² (u - ) du

A:

Q: Determine the radius and interval of convergence of the following power series. k X ()* 12 M8 k=1…

A:

Q: Use Taylor series you already know to find the Taylor series generated by f(x) = x sin(6x) at x = 0

A:

Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

A:

Q: y=x5, mn=-1/80

A: Given problem:- Find the equation of the line normal to a given curve y=x5 and having a given slope…

Q: Consider the matrix A= Calculate a31 Calculate 932 755 826 5 2 6 e 9 dh n bf a

A:

Q: 1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a…

A:

Q: 1. a) Copy the graph. YA 4 2 4-20 2 f(x) AR 2 4 x (g(x) b) Use the superposition principle to…

A:

Q: 2. 3. (32²+7)dx=(2,₁¹²₁ )dy = 0 4) 1 xe²x dx + (5-1)dy = 0, y(0) = 0 1

A:

Q: 5x+3 2x² + 4x+7 -2 dx

A:

Q: y 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6 X

A: We can find the Domain and Range of the function.

Q: EX #3: Roller Coaster A hypercoaster is a special circuit roller coaster with a height measuring…

A: A hypercoaster is a special circuit roller coaster  with a height measuring greater than 200 feet.…

Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: e) fx³ √2x² +1 dx wil(-) {. ub f CP

A:

Q: What is the radius of convergence of the series R=2 b. R=1 R = ∞ d. R=0 a. C. +∞ xn n+1 -?

A:

Q: Given |F₁ = 85 N and |F₂| = 125 N and they are acting at an angle of 14 a) Find the magnitude of the…

A: Topic:- application of vector algebra and trigonometry

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

A:

Q: (iv). limit x-0 ²-1 - x - x ²³/₂2 - x² - x ²%/ e 6 x4

A:

Q: 3. f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(2x)]. The table below…

A:

Q: 1. cos50 sin³0 de TL 2

A:

Q: If f(x) = f'(x) = 4-3x7, find f'(x). Use exact values.

A:

Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

A:

Q: Determine whether the following relation represents y as a function of x. -6-5-4-3-2-1 y 7r 6 L 5 4…

A: