lim Δx→0 3 1 x + Δx Δε 1 της X

Q: 8. Consider the function F(x) = f, 3x² - 4x +7 dt. Find the equation for the tangent line to F(x) at…

A: The function is Fx=∫-1x3x2-4x+7dx.To find : Find the equation for the tangent line to Fx…

Q: Consider the following vector function. r(t) = (8 sin(t), t, 8 cos(t)) (a) Find the unit tangent and…

A: To find unit tangent and unit normal vector and curvature. Given  r( t) =  { 8sin(t), t, 8cos(t) }

Q: 6) The velocity of an object on the interval 0 ≤ t ≤ 10 is shown in the graph below. If v(t) is…

A:

Q: QUESTION 4 Determine the number of triangles with the given parts. b= 10, a = 65°, y = 132° 0 1 2…

A:

Q: 6. Consider the following graph of the function f(x) = cos(x). Draw on top of the graph to indicate…

A: Here we have given a function: f(x)=cosx. a) The limit that will compute the exact area represented…

Q: Construct a limit evaluation problem with an answer of 1. (do not use L'Hospital's rule)

A:

Q: The graphs of f(x) = x²-3x - 4 and g(x) = -2x - 2 intersect at the point (-1,0). The (acute) angle…

A:

Q: Determine if the vector pair are orthogonal or not. a = 6i 18j and - b = -8i + 3j

A:

Q: Find the area between y = 6 - ² and y = x² 2 -5 -4 N 8+ 7 3 2 -1 -2 -3 The area between the curves…

A: The equation of curves are given y=6-x2 and y=x22-4

Q: Use the equations to find дz Әх az ду - дz Әх əz Әх = and ƏF Әх ƏF əz and дz ду əz ду x2 - y2 + z² -…

A: x2-y2+z2-6z=7∂z∂x=-∂F∂x∂F∂z∂z∂y=-∂F∂y∂F∂z

Q: 6. For what value(s) of k, does the function f(x)= Aex where A is some constant, satisfy the…

A: The given function is: f(x)=Aekx  ;       where A is some constant.

Q: Solve the differential equation. 5√xy dx = dy dx = 2, x, y>0

A:

Q: Function f(x) is positive when 1<x<2, and it is negative when 2<x<3. If the area of the region…

A: If Function fx is positive in a,b∫abfxdx=Area under the curve fx over inteval a,bIf Function fx is…

Q: 7. In the two questions that follow, the function f(x)=b* is an exponential function. Think…

A:

Q: 2 X 2 [√³² L √ ² - ²³ √ x² + ²³² dy da dx 0 X

A: ∫0√2∫x4-x2x2+y2dydx

Q: Evaluate the following indefinite integral. de = +0 ds +C

A:

Q: Use Part I of the Fundamental Theorem to compute the integral exactly. 1₁ (x + 8x)dx=

A:

Q: Use the Integral Test to determine whether the infinite series is convergent. To perform the…

A:

Q: The strength of magnetic force varies inversely with the square of the distance between the magnets.…

A: Force is given by÷ F=kx2  When both the magnet are 6 cm(0.06 m) apart there is a force of 4N.…

Q: Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given…

A: Given: Polynomial f(x) has a leading coefficient of 1, has a degree of 7 andhas roots 4,5,3-i and…

Q: Write the vector below in trigonometric form. m = −10i +10j m = 4√5 m = 4√√5 m = 10√/2 m = 10√/2…

A:

Q: Express the limit as a definite integral on the given interval. 2 lim Σ 19(x;*)3 – 5xi]Δx, [2,7] i =…

A:

Q: Find the standard form of the complex number 6 (cos+ i sin). Round values to the nearest hundredth.

A: Standard form of the complex number is a+ib , where a ,b are real numbers.

Q: 1. The electrical power p(t), in kilowatts, being used by a household as a function of time t, in…

A: p(t) = power in kilo watt t = time

Q: Evaluate the integral. π [" 10 3x³ cos(x) dx

A: To solve the given problem, we will use following integration formulae ;

Q: You know that: ■ ■ ₁9(t) dt = 15 g(7) = g(9) = 5 Evaluate: +9 юст g'(x) √√25-(g(x))² Upload your…

A: Given:  ∫79gt dt=15g7=-52g9=5 To Find: To evaluate the integral ∫79g'x25-gx2 dx.

Q: 7) Find the area bounded by the line y = x and the parabola x = y² - 2y.

A: We know that the area formula int_a^b {f(y)-g(y)} dy

Q: Calculate S3, S4, and S5 and then find the sum for the telescoping series where S is the partial sum…

A: Given: S=∑n=2∞ 1n+1-1n+2 To find the S3,S4,S5,S.

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A:

Q: Find all the second partial derivatives. f(x, y) = xy - 4x5y² fxx(x, y) = fxy(x, y) fyx(x, y) = =…

A:

Q: If f(x, y, z) = 3xy²z³ + arcsin(x√√z), find fxzy. [Hint: Which order of differentiation is easiest?]…

A: fx,y,z=3xy2z3+arcsinxz

Q: If f(x) da = 16 and ¹ Answer: fr f(x) dx = 3.1, find f(x) dx.

A: We know that the formula int_a^b f(x) dx=-int_b^a f(x) dx

Q: 2. Find F'(x) if F(x) =tan(3x² + 2x). Solution: U= du dx 11 dy du dy dx 11

A: As per our company guidelines we are supposed to solve first question in different questions so…

Q: Use the Integral Test to determine whether the infinite series is convergent. 8 n=1 -n² 16ne

A:

Q: Compute the partial sums S2, S4, and S6. S2 = S4 = S6 = 3 1.2 + 3 3 + 2.3 3.4 +...

A: First we find the sops of given sequence.

Q: (c) Figure 4.1 shows the rough sketch of the function: y = x(x² - 6x + 8) y 0 A Figure 4.1 B X Find…

A: NOTE: Refresh your page if you can't see any equations. . to find the zeros of the function, take…

Q: 12-0 dt = + C

A: We know that the integral of x^n dx = x^(n+1)/(n+1)

Q: 10) Write an integral function that represents the velocity of an object at any time t given the…

A: The acceleration of the object at any time t is at Initial velocity is v1 To determine: An integral…

Q: I. Evaluate the double integral 5 2x SS 0x (3x + 2y)dydx

A:

Q: Estimate the number of flashlights that can be sold at $5. Round your final answer to the nearest…

A: The data of x vs f(x) is given as Sr. No. x f(x) 1 6 86 2 12 60 3 18 38

Q: Construct an equation that has an absolute maximum of 5 when graphed. Please show steps.

A:

Q: Given f(x) = 3x + 7 9x² 5 A) Find lim f(x) ° x→∞ B) Find lim f(x) ° x118

A:

Q: Find the area of the region under the graph of the function f on the interval [-27, -1]. f(x) =…

A: we need to find the area under the graph of the function fx=5-x3, from -27≤ x≤-1.

Q: 5. Integrate (a) [² 3x +7 dx + (b) fe' de (c) [5-13dt (Note your answer should have z in it. )

A: The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Find all angles in [0°, 360°) that satisfy the equation. √3 sin 0 = O {60°, 300°} O {150°, 210°}…

A:

Q: 1 Given that sin A = and tan B = 1, and that angles A and B are both in Quadrant I, find the exact…

A: sinA=126 and tanB=1 ,A and B in Quadrant I

Q: The average value of f(x) on the interval (a, b) is found by using the following equation. 1 fave =…

A: The given function is: f(x)=4x-x2 ;          0, 4

Q: 3 Find the derivative of y=In (8x³-5x)

A:

Q: 3) Refer to the information in Problem 2. Find the distance traveled by the object for the interval…

A: We have, Vertical position:    y(t) = 32t - 8t2  Interval:  0 ≤ t ≤ 3

Q: Calculate all four second-order partial derivatives of f(x, y) = 4x²y + 8xy³. fxx (x, y) = fay (x,…

A: