Use words to describe the formula for, "Without showing algebraic details, describe in words how to reduce the power of cos4 x."

Q: Find the inverse of the function. f (x) = 5 – 2a3

A:

Q: Calculus Question

A:

Q: If it is known that ∫51f(x)dx=−3 and ∫52f(x)dx=4, find the value of ∫21f(x)dx.

A:

Q: Find the standard form of the equation of an ellipse with foci at (-2, 0) and (2, 0) and vertices (-...

A: Standard form of an ellipse whose center is origin: x2a2+y2b2=1          ...(1) Where the coordinate...

Q: Find all values of 0 in the interval [0°,360°) that satisfy the equation. Use degree measure. 49 sin...

A: Given that, the equation is 49sin2θ+84sinθ+36=0 and θ∈[0°,360°). Compare the given equation into the...

Q: Differentiate f(x)=√1−x2 by evaluating the limit of the difference quotient. Show all steps, using c...

A: Using the limit of the difference quotient we get: limh→0f(x+h)-f(x)h=limh→01-(x+h)2-1-x2h

Q: What is the last term in the expansion (2xy z+3x²y)4?

A: Consider the provided expression, 2xy2z3+3x2y4 Write the last term of the expression. Apply the bino...

Q: Given several terms of a sequence fan} 1 complete parts a. through c. below. 00 {4, 6, 8, 10, 12, .....

A: The given sequence is = {4,6,8,10,12} Here the common difference=2so the next two terms are a6=12+2=...

Q: ) Find the linear approximation, L(x), of at x = 9. Use this to approximate f(11).Do you think your ...

A: Let take a function: fx=x The linear approximation can be calculated as: Lx=fa+f'ax-a  ................

Q: Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r

A: Let the length of the rectangle be 2x and the width of the rectangle be y. From the figure, the exp...

Q: cos²(x) dx 1+ sin(x) Evaluate:

A: Using the Pythagorean identity we know that cos2(x)=1-sin2(x)So, ∫cos2(x)1+sin(x)dx=∫1-sin2(x)1+sin(...

Q: Determine if the integral converges or diverges. If it converges, give its value. re+3 1 dx 2 (3- x)...

A: Let us consider the given integral I as: I=∫2e+313-xln3-xdx Let us make substitution by putting u=ln...

Q: The circumference of a circle is increasing at a rate of 2 cm/s. How fast is the area increasing whe...

A:

Q: I need to find how fast , in radians per second, will the gun have to turn to accurately track the a...

A: Given that, The height of the aircraft is 110 ft. Let x be the distance from the gun to the point on...

Q: Find the exact value(s) of all numbers that satisfy the mean value theorem for f(x)=9√x−5 on [1,9]. ...

A:

Q: Solve the differential equation (t^2 + 2t)dx/dt= 2x + 2, using the initial condition x(1) = 1. Your ...

A: The given differential equation - (t2+2t)dxdt=2x+2dxdt = 2x+1(t2+2t)Separating variables - dxx+1=2dt...

Q: These are true or false questions.

A:  Since you have asked multiple questions in single request  so we  will be answering only first ques...

Q: This is a Calculus 3 problem. Please explain b) clearly, no cursive writing.

A: fx, y=-x2y2x2+y2 Now, z0=fa, b=f1, -2=-12-2212+-22=-45 Now partially differentiating fx, y=-x2y2x2+y...

Q: Convert (−2, −9) to polar coordinates. (Let r > 0, 0 ≤ ? < 2?.) (r, ?) =

A:

Q: In someone infected with measles, the virus level N (measured in number of infected cells per mL of ...

A: The area under the graph of Nt from t=0 to t=12.

Q: Find the absolute extrema of the function on the closed interval. y = x ln(x + 6), [0, 3]

A:

Q: In Example 6 in this section, we were given fx) = 3x? + 2x + 11 and found rx) = 6x + 2. (a) Find the...

A:

Q: Set up an integral to find the length of the curve defined by y = 4x2 – 3 from x = 3 to x = 9, then ...

A:

Q: For the differential equation below please provide the undetermined coefficients function you would ...

A:

Q: prove the following version of the First Derivative Test: If f′ is continuous on the interval [a,b] ...

A: To Prove: If f' is continuous on the interval a,b and if f​ has exactly one critival point c then fu...

Q: Can you help me find the integral of this problem?

A:

Q: Find. d? (® Int) dt

A:

Q: Determine whether the following series converges. Justify your answer. (- 1)*k Σ 9k +1 00 k= 1

A: The given series is an alternating series and not a geometric series. So we will ignore the geometri...

Q: Determine how many terms of the following convergent series must be summed to be sure that the remai...

A: We know                    Error = Rn≤an+1 where an+1 is the magnitude of n+1th term in the sequence...

Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 = 0...

A:

Q: determine all critical points and all domainendpoints for each function. ƒ(x) = 6x2 - x3

A: given function f(x)=6x2-x3 we have to determine the critical points and domain endpoints for the fun...

Q: Suppose that ff is a function such that f(−1)=12, f'(−1)=−7, and f''(x)=6x+8. Find each of the follo...

A: f"(x)=6x+8f'(x)=∫(6x+8)dxf'(x)=3x2+8x+CGiven f'(-1)=-7 so, f'(-1)=3(-1)2+8(-1)+C-7=3-8+C-7=-5+CC=-2S...

Q: Find the derivative of the function f(x) = In(2a? + 5æ)

A: ddxln (x)=1xddxxn= n xn-1  

Q: DEF only please i did abc

A: The points A2,1,3 and B4,4,1. Let a→ and b→ be the position vectors for coordinates A and B. Let c→ ...

Q: dy is Blank 1 dx Given y-xy2-x²y=2. Then, at the point (1,2), Blank 1 Add your answer

A: Determine the differentiation of the given equation. 3y2dydx-y2dxdx·xdy2dx-x2dydx·y·2x=03y2·dydx-y2-...

Q: I need some help on my hw.

A:

Q: Find all values of x for which the tangent line of f(x) = V x2 + 18x + 96 is horizontal.

A: Given that, the tangent line horizontal. That is it is parallel to x axis. The equation of the tange...

Q: Find the domain and range of the function. f(x, y) = v 64 – x² - y? Domain: + y? o {x, v): x² + y? 2...

A:

Q: Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (...

A: Surface equation - So there will be two planes passing through 3,4,5 and -4,-3,5The equation of a pl...

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice...

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change ...

Q: Find the second derivative of f(x)=x^2-3/x.

A:

Q: I'm having a hard time setting up the integral for this one. Please help!

A: Given: y2=x4-x2 To Find: a. Which approach is better for the task verticallyusing dx or horizontally...

Q: Consider the equation below. 7-6 sin(@) (a) Find the eccentricity. (b) Identify the conic. O ellipse...

A:

Q: Use implicit differentiation to find the derivative of arctan(x).

A:

Q: If f(x)= x/1+g(x^2), and g(4) =0, g'(4) = -1, then f'(2)=?

A: Some rules of differentiation which you will use in solving this question: ------------------------...

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.