Suppose that h(x) is an unknown function with the following properties: ex x² ● h'(x) - h(1) = 3 Use this information (and integration by parts!) to calculate [²x.h(x)

Q: For what value of b does the limit b = exist? What is the value of the limit? b = b b b = = lim x→→2…

A: Limx--2(6x3+5x2-12x+b)/(x2+x-2) Find the value of b and the limit.

Q: What is the component form of the vector represented by 6a when a = (-2, 3)? 6a =

A:

Q: 5. Determine if the given function f(x)=x²-1 if x ≥ 1 (x+1 if x < 1 is continuous at x = 2?

A: According to the bartleby guidelines we supposed to do the first one of multiple questions kindly…

Q: X Find the derivative of y = x • xx−1 X. x ln(x) x* (ln(x) + 1) In(x) + 1

A:

Q: Describe how these planes intersect. If they don't intersect explain why. T₁: 5x 10y + 20z - 10 = 0…

A: The equations of the given planes are,REQUIRED :We have to find whether the given planes intersects…

Q: If ƒ(4) = 3 and fƒ'(4) = −5, find g'(4) where g(x) = √xƒ(x).

A: To find g'(4) where g(x) = sqrt(x).f(x)  also given f(4)=3 and f'(4)=-5Derivative using product rule…

Q: 38. f, f(x) dx where f(x) - -{-x if -24x50 4-x² if 0<x<2

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Q: Given the following piecewise function, find the values of a and b so that the function is…

A:

Q: We can calculate w by determining the distance per second. What is the rate of the revolution for…

A: Formula for the angular velocity is as follows Where N is the Rate of revolution is the angular…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 8.…

A:

Q: Consider the plane with a scalar equation 4x-2y+z-19=0. Find the point of intersection of this plane…

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Q: State the range for the function: ƒ(x)=-log₁(x−1)+2 O (-00,00) O (-∞, -1) O (0,00) O (-00,0) 82°F…

A:

Q: Use the disk method to find the volume of the solid of revolution bounded by the x-axis and the…

A: Region bounded by x-axis and Using Disk method , Volume of solid of revolution about x-axis will be

Q: Estimate the slope (slope = rise/run) of the tangent line to the curve. 10 9 8- 7- -6- 5- -1 0 N. -3…

A: (i) To estimate the slope of the tangent line to the curve in the following figure.(ii) To estimate…

Q: Draw a sketch of the graph of f(x) = 2√x + 1 − 1. Explain the trans- formations of the graph of…

A: Explaination of the answer is as follows

Q: Given the graph of f, what are the point of inflections? check all that apply 1 X=1 x=2 x=3 X=4 x=5…

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Q: A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the…

A:

Q: tan (sin ¹(-)) cos (tan ¹(1)) Enter your answer, as a simplified fraction, in the box. What is the…

A: let

Q: A well stirred tank originally contains 100 gal of fresh water. Then brine containing 1/4 lb of salt…

A:

Q: For each of the following integrals find an appropriate trigonometric substitution of the form x =…

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

Q: Let f(x) = 11x³ over the interval 0 ≤ x ≤ 1. Set up the integral for the surface area generated by…

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

Q: The DNA molecule has the shape of a double helix (see the figure below). The radius of each helix is…

A: The radius of each helix is about 10 angstroms(1 Å = 10–8 cm)Each helix rises about 34 Å during each…

Q: Which slope field is associated with the differential equation given below? dy dx = 1-y Choose the…

A:

Q: Determine the intervals where the following functions are continuous. 3. f(x) = √25-x² 4. g(x)= x²-9

A: Continuity of a function:A function is continuous at a point if the function is defined at that…

Q: 5. The vertices of parallelogram ABCD are: A(3, -2, 4), B(-2, 0, 5), C(3, -5, -4) & D(x, y, z). a)…

A:

Q: lim (9X+1) ² X→-1

A:

Q: Find the derivative of h(x) 3 4 sin x COS X sin x COS X 2 COS X 1+ sin x - 3 cos²x (1 + sin x)³ 2…

A: To find the derivative of .

Q: if both f (x) and g (x) are differentiable, then d d [ƒ(x). 9(x)] = f'(x). g' (x). O True O False

A: given both f(x) and g(x) are differentiable.

Q: 1. Use the graph off to state the value of each statement if it exists. a. lim f(x) C. X→-1- b. lim…

A: Existence of limit at a point:We know that for limit to exist at any value of x, say x=c exists only…

Q: State the domain for the function f(x) = log₁(x - 5) + 4: O (5,00) O (-00, 5) O (-00,00) (0,00)

A: We have to state the domain for the function

Q: (A) Find the average value of the function over the indicated interval. (B) Graph the function and…

A:

Q: Find the first partial derivatives of the following function. 8u 5v + 7w F(u,v,w)= F₁ = Fu

A: given

Q: Find the area of region bounded by generated curves. Do not forget to show your graph. 9. R is the…

A: We are required to find:

Q: if f'(a) exists, then f is continuous at x = a. True False

A: Function f differentiable at x=a

Q: Given f(x) = 2x² + 1 and g(x) = 4x - = 4x - 6, find the following. (a) f(g(2)) (b) f(g(x)) (c)…

A: Given functions are,Under guidelines we are suppose to answer only 1 or 3 sub parts.

Q: 4x³-13x²+3x+2 x²-4x+3 dx

A: I=

Q: What is the rectangular form of the polar equation r = 4sin(0)? Choices: x = 4sin(0), y = 0 x = 0, y…

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Q: Integral 2 25x²-81 S X -dx

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Q: Evaluate the limit, if it exists: xy lim (x,y)+(1.1) x² + y²

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Q: If R is the region between the graphs of the functions f(x) = 4x³ + 9x² + 7x-3 and g(x) = 5x³ + 2x²…

A: Two function are given÷f(x) = 4x3+9x2+7x-3g(x) = 5x3+2x2+17x-3We need to find the area between the…

Q: Given the initial condition y(0) = 2, find the particular solution of the equation e'y' - 2x = 0

A:

Q: d the derivative dr do for r 2007 cos 0 =

A: We find derivative value.

Q: Use the graph off to state the value of each statement if it exists. y = f(x)

A: The function of f(x) is given.As per guidelines, At a time only three sub-parts of a question can be…

Q: What is the exact value of a trigonometric function of a given angle? Select True or False for each…

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Q: y" - 6y' + 8y = 0

A:

Q: the

A: Solving the problem

Q: dQ Use the Chain Rule to find where Q=√√4x²+4y² + 2z², x = sint, y = cost, and z = cost. dt 7 dQ dt…

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Q: 2. The minimum depth, d (in meters) of water in a harbour, t hours after midnight, can be…

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Q: Find all the second partial derivatives. sin(3s² - 4t²) V =

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Q: Prove the formula for d dx d [arccos x] in the same manner used for [arcsin x] in class. dx

A: