Find the derivative f'(x) of the following function. sin x e2x [A] [D] cos x−2 sin x e2x 2cos x+sin x e2x [B] [E] cos x+sin x e2x f(x) = 3cos x-2 sin x ex [C] cos x−sin x ex

Q: Using the Second Derivative Test, where applicable, find all the relative extrema of f(x) = 12x³ −…

A: Let's find relative extrema of given function.

Q: Find the vector needed to translate from point (4,1) to point (8,3). Translate (-1,2) by the same…

A:

Q: d. y'= 1+y² 1+t² y(0) = -1

A:

Q: Find the centroid of the quarter of the unit circle lying in the third quadrant. ICM усм

A: The equation of the circle is x2+y2=1 The radius of the unit circle is 1 unit.

Q: Question Let h(x) = f(x)g(x). If ƒ(−6) = 4, ƒ' (−6) = −2, g(−6) = 2, and g'(-6) = 5, what is h'(-6)?…

A: Use product rule of differentiation.

Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

A:

Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: Topic -Application of derivatives We are given a cardboard of 20 inch by 32 inch and we need to find…

Q: Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least…

A:

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

A:

Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction and at the…

A: To find directional derivative of given function.

Q: The auxiliary equation of y"" - 4y" - 4y' + 16y = 0 is r34r²4r + 16 = 0. The auxiliary equation has…

A: Given; f(r)=r3-4r2-4r+16 , [-0.75,3.75].

Q: Calculate the first four partial sums of the given series, S₁, S2, S3 and S4. Also, determin whether…

A:

Q: The independent variable x is missing in the given differential equation. Proceed as in this example…

A:

Q: Find the centroid of the region lying underneath the graph of the function f(x) = e over the…

A:

Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

A: Remember that: Time t is taken on x axis and velocity is taken on y axis. The particle moves forward…

Q: Find the derivative of: Ř(t) = (sin² (3t + 1), ln(t² − 1), ²+1 –

A:

Q: Evaluate the following integral. 2x + 5 2 x + 25 X 2x + 5 2 x + 25 dx dx =

A:

Q: [(x² +1) cos +=dx 2

A:

Q: Suppose the fridge daily cost function produced at Friga's Frigid Fridges is represented by the…

A: GIven Cost function:- Cx=x32000-x250+50x+20,000

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = [0, 9] X x²…

A: topic - Application of derivatives We are given, f(x)=xx2+25  ,[0,9]we know…

Q: Answer is incorrect

A:

Q: 63-68 Find the slope of the tangent line to the given polar curve at the point specified by the…

A:

Q: Find the domain of the following vector-valued functions. Š(t) = (tant, √4-t², =) 2+t

A: domain of tan t is 'all real numbers';   The domain of tan t is all real numbers except for…

Q: Consider the following autonomous first-order differential equation. y' = y² + 2y 1194994 ++ + + +

A: Given differential equation y'=y2+2y

Q: which one of the following is the same as: -cos(-x)tan(-x) a. sinx b. -sinx c. -cotx

A:

Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: We know that polynomial has degree n if it has n x intercept and polynomial has degree n if it has…

Q: Perform one step of row reduction, in order to calculate the values for x and y by back…

A:

Q: Find the equation for a polynomial f(x) that satisfies the following: Degree 3 ■ Zero at x = -2 ■…

A:

Q: Let y = f(x) = 6x³ + 13x - 13 and g the inverse function of f. Note that f(1) = 6. Find the value of…

A:

Q: If lf Ŕ(t) = et cos tỉ – et sin tj Find the velocity and acceleration vectors.

A: To find the velocity and acceleration vectors for the given position function.

Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: Find the exact value of each trigonometric expression. For each part state the quadrant or axis that…

A:

Q: 7. List all critical points of g(t) = (t - 3)et -t(t-4).

A:

Q: x 9 PCRS (57) thenewboston YouTube A31 W6 Complete Lectures.pd C…

A:

Q: Consider the shape with vertices (1,3),(4,7),(0,10),(-3,5) translate the rectangle so (1,3) lies on…

A: We need to transform the coordinates.

Q: the reference angle of an angle -145 degree?

A: We have given angle  Let, θ=-1450 Coterminal angle is given as θc=3600-1450 θc=2150 So, θ=-1450 lies…

Q: Calculate directional derivatives and gradients in three dimensions. Find an equation for the…

A:

Q: Determine R(t) if R'(t) = <2e2+-4,4 =-1) and R (2) R (2) = <3₁-5,0).

A: To determine R→t if R'→t=2e2t-4, 6t2, 1t-1 and R→2=3, -5, 0.

Q: Step 3 Now write the derivative in terms of x by recalling that u = -3x + 7 and v = x + 7. du 1 +=…

A:

Q: 4. Find an equation of the tangent plane to the surface xy + yz+zx = 3 at the point (1,1,1).

A:

Q: Evaluate the following integral using integration by parts. fxsin 6x dx

A:

Q: Given vectors from the origin r = 3a, + 8a, +a, r=a, -6a, + 5a,, and rc = 7a, - 48,, find: (a) a…

A: The cross product two vectors, say a= a1ax+a2ay+a3az and b = b1ax+b2ay+b3az denoted by a×b is…

Q: b) Is the integral in de convergent? Explain why! I

A:

Q: State the equation of the rational functions whose graph is below. y 5+ 4+ 5432 3+ 2+

A: NOTE: Refresh your page if you can't see any equations. . as we can see  from the graph, the…

Q: Parameterize boundary of triangle (0,0),(5,0),(3,9)

A: We can parameterize the triangle in the below steps.

Q: Find the transform of the given function by use of a table. f(t) = 4t³e²t 24 (s+2)4 (B) There is no…

A: We have to find the transform of the function  ft = 4t3e2t.

Q: Only

A:

Q: dy Find for the equation ex+y² = x. dx 3-x [A] [B] ³ xy 1-x 2xy [C] 1-2x xy [D] 2-x 2xy+e [E] 1-x xy

A: Concept: The formulas used: ddxxn=nxn-1ddxln(x)=1xln(ab)=bln(a)

Q: The general solution to the DE in the initial value problem (IVP) (y" + 8y' +16y = 0 y(0) = 1 y'(0)…

A:

Q: 2. Determine f'(x). (a) f(x) = √26

A: