(b) π/4 (sin(x) = cos(x)) (sin(x) + cos(x)) dx

Q: if f(x) = x sinx, then f'(x) = sin x + xcosx. show that there must be at least one value of in the…

A: The given function fx=x sin x and its derivative is f'x=sin x+x cosx. We have to show that at least…

Q: The line that is normal to the curve x² + xy - 2y² = 0 at (5,5) intersects the curve at what other…

A: Topic = Application of derivative

Q: Solve the following DE. ( Variable Separable )  1. y' = cos2x cosy

A:

Q: Let f(x) = mx - 11 ²+10x-8 if x < -3 if x ≥-3 If f(x) is a function which is continuous everywhere,…

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Q: Question 9 Determine whether the DE has homogeneous coefficients. If so, find the implicit solution.…

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Q: 1. f(x) = 4 sin x cos x 2. g(x) = 3 sinx - x cos x 3. h(y) = cos y cot y

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Q: The graph below is the function f(x) -5-4-3-2 • 16 9 14 2- 1 - di ON m A 1 2 3 Find lim f(x)= 2--1-…

A: Topic = Limits

Q: Sketch a graph of f(x)=x+1 1 -5 -4 -3 -2 -1 5 4 3 2 1 -1 1 if -1 1 2 3 4 5 -3 -4 -5 Clear All Draw:…

A:

Q: Find f'(x) and f''(x). 2 x - 5x x+1 f(x)=

A: Given: f(x)=x2-5xx+1

Q: Find the slope of the tangent line to the graph of the function at the given point. f(x) = 9x - 4x²…

A: To find out the slope and equation of the tangent line.

Q: -52 The region R in the first quadrant is bounded by the coordinate axes, the curve y = e x = 1. The…

A:

Q: What is the orientation of the equation of an ellipse below? y² x-² 2.25

A: Solving the following problem

Q: Use logarithmic differentiation to find the derivative of y with respect to the given independent…

A: Please see the below picture for detailed solution.

Q: 5. What is the change in surface area with respect to time at t = 4s? Given that 12t^5 cm^3/s

A:

Q: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

A: The displacement (in centimeters) of a particle moving back and forth along a straight line is given…

Q: 3. (x + y - 6)dx + (x − y + 4)dy = 0.

A:

Q: .A rectangular fence is to be constructed with one of its face adjacent to an existing wall. Given…

A:

Q: Suppose a company that makes lava lamps is trying to determine how to increase profit.  They find…

A:

Q: let r(t)=(t^2,1-t,4t), d/dt[r(t) dot a(t)=?, t=2 ,assume that a(2)= and a'(2)=

A:

Q: If = -87, then find exact values for the following. If the trigonometric function is undefined for…

A: Theta=-8pi

Q: Find the unit tangent vector to the curve at the specified value of the parameter: r(t) = 7+₁ -In(t)…

A: Given data Find the unit tangent vector to the curve at the specified value of the parameter:…

Q: Find the periodic withdrawals PMT for the given annuity account. (Assume end-of-period withdrawals…

A:

Q: a. f(x) = 15x²-3x-5 + c. f(x) = a. 1 x2 x³ + 2x² - 9x +5 X 4. Write the equation of the tangent line…

A:

Q: Suppose C(x) = g(t)dt where the graph of 0 g is given below. tu 0 X True 5 False 10 True or false:…

A: Suppose Gx=∫0xgt dt, where the graph of g is given below. To determine whether the following…

Q: The force F on an object is the product of the mass m and the acceleration a. In this problem,…

A: F(t)=m(t)a(t) at t=7 s,  m(t)=51 gramschanging rate=m'(t)=9 gsat t=7, a(t)=8 ms2  changing…

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: Given query is to find derivative and the slope of the tangent.

Q: Discuss the continuity and sketch the graph. 1. f(x) = 3x² + 2x + 1, x = -2 2. f(x) = x² - 4x+4 x-2…

A: We have to discuss the continuity and sketch the graph  (1) f(x) = 3x2 + 2x + 1, x = -2

Q: Find a non-trivial linear combination of a, b and c whose sum is the zero vector. 0 a+ b+

A: Given from the graph, a=&lt;-8,-2&gt;,   b=&lt;5,-8&gt;,   c=&lt;-5,-6&gt;

Q: If f(x) = 3√x (x³ - 5√x+4), find f'(x). x ²7/31²- Find f'(3). X

A:

Q: If f(-3) = -6, f'(-3) = -5, f(-1) = -18 and f'(-1) = -12 then: [ x . f"(x) dx

A: Given:- f-3=-6,f'-3=-5,f-1=-18,f'-1=-12

Q: 3. Estimate the area of the finite region between f(x) = -x and g(x) = by summing the areas of n…

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Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

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Q: 사 In a certain year, the average e-mail user sent or received 157 e-mails each day. The number of…

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Q: əz dz Express and as functions of u and v both by using the Chain Rule and by expressing z directly…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 3x3. (Use…

A: We have to find the surface area of revolution about the x-axis over the interval [0,1] for y=3x^3.

Q: Select any necessary conditions for a function to be differentiable over its domain.   Question…

A: We know that a smooth function is a function that has continuous derivatives up to some desired…

Q: Find the volume of the parallelepiped determined by the vectors a=, b=, c=   Please make easy to…

A: Here we have to find the volume.

Q: 25

A:

Q: Let f(x) = 8x³ - 15x²2 -2, x ≥ 1.5. Find the value of 3 df The value of df 1 at the point x = 623 =…

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Q: (3y^3 - 5yx^2 )dx + (xy^2+ x^3 )dy = 0 ; x=1, y=2

A: Given differential equation:- 3y3-5yx2dx+xy2+x3dy=0

Q: Evaluate the limit lim s→6 1 S 1 6 S-6 -

A:

Q: Find the limit. lim x+0 sin² (7x)

A: Given query is to find Indicated limit.

Q: 1. Consider the following, recursively defined function C(1) = 1 C (2) = 1 - C(n) = C(C(n − 1) + C(n…

A: We need to prove that C(n)=1 for all n.

Q: Given f(x) = 761x - X if 0 ≤ x ≤ b if b < x a) Determine a value of b so that the function given is…

A: Given:  fx=x2-7 if 0≤x≤b6x if b&lt;x To Find:  (a) To determine a value of b so that the given…

Q: -50x7 - 30x6 - 20 5x² Type your answer without negative exponents. Simplify completely. Find the…

A: Given the quotient function is -50x7-30x6-205x2

Q: Find the directional derivative of f(x,y,z)=-4x2+2y2-3z2 at the point (1, 4, 5) in the direction of…

A:

Q: 15 -3 -2 -1 2+ 4 3 N -1 -2 -3 -4 2 3 JA -5+ In the above graph of y = f(x), find the slope of the…

A: Solution:

Q: D Question 5 let g(x) = 1/(x³+x²)3 find g'(x) O(x³+x²)3 O (x³+x²)-3 O-3 (x³+x²)-4(3x²+2x)…

A:

Q: Suppose f(z)-(2-10)(z- 0)(z+8). a. Determine the roots of the function f. Preview b. What is the…

A:

Q: Find the distance in netween the point P(-4,3,-1) and Q(4,-1,3)

A: given points P(-4,3,-1) Q(4,-1,3)formula for distance is D=(x2-x1)2+(y2-y1)2+(z2-z1)2