t – 1 Vt + 3 i + tan t k lim t→1

Q: Consider the function f(x, y) = 8x? – 5y? + 4xy over the unit square 0 <x < 1, 0 < y < 1. NOTE: Ente...

A: Please consider the handwritten solution.  

Q: 3. Draw a picture of an even function and a picture of an odd function. You can use Desmos or draw b...

A: Using f(x) = x2  and f(x)= x3, 

Q: Given that f(7) = 1 and f'(7) = -7, find an equation for the tangent line to the graph of y = f(x) a...

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Q: Example 1. Let f(x, y) = (y + 1)e²+v°, (a) Find the tangent plane to f at the point (0,0).

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Q: Check the alternative that best applies to the function of two variables whose graph is given: a. f...

A: So, in this graph, if you could look closely and try to see the projection on the yz plane, you can ...

Q: Solve the given differential equation. (y + 2xy°)dx + (1 + 3x²y² + x)dy = 0 2.3 Oxy + x´y° – y = c |...

A: this is the question of differential equation .solve in step 2.  

Q: .x = t² – 2t – 11 and y = t(t – 4)³ – 3t²(t – 4)² + 7

A: Given:- x = t² - 2t - 11 and y=t(t-4)³ - 3t²(t-4)² +7 To find:- y' 

Q: 4. We have 45 square meters of material to make box with square base and no top. We want the maximum...

A: For the solution of the problem follow the next steps.

Q: 1. Consider the van der Waals equation (1) a (p+ v2) (Vm – b) – RT = 0 V2 т where p, Vm, T, are, res...

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Q: Show that one of the lines givenby 6x - xy -12y = 0 coincides with one of the lines givenby 15x² +14...

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Q: If H(x) = log, 1/x, show that H(b) = 1/z. %3D %3D

A: Given, Hx=logb1x We have to show that Hb-1z=1z 

Q: 5. f() = {x? - 4 U x* -3 Evaluate f(4), f(0), f(-3) and f(-2/3) }" -2 if x = -3'

A: The objective is to evaluate f(4), f(0), f(-3) and f(-2/3). 

Q: F(r, y) = is a homogeneous function of degree 1. True False

A: We have to check degree of homogeneous function.

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =...

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Q: and of b is Writing the complex number z=2 e6 in the form a+ ib, the value of a is

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Q: Integrate the function. Use trigonometric substitution. dx V9 -x2

A: The trigonometric substitution used is x=3 sin θ

Q: If the chord joining two points (a sec 0,, b tan 6,) and (asec 0,, b tan e,) x² passes through the f...

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Q: Current Attempt in Progress Find T(t) and N(t) at the given point. x = e' cos t, y = e' sin t, z = e...

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Q: Let s(t) = 6t - 54t2 + 144t be the equation of motion for a particle. Find a function for the veloci...

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Q: 3. Find the maximum volume of all possible cones that can be inscribed in a sphere of radius 3. Reca...

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Q: Question 6 of 10 > Find the minimum and maximum values of the function y = 3x? – 6x + 5 on the inter...

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Q: ariable cost per item: $27.50 rice at which the item is sold: $27.80 Part: 0 / 4 Part 1 of 4 (a) Wri...

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Q: ) Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional ...

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Q: Find the area of the region bounded by the curve y=x^2−1 and the line y=15.

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Q: Evaluate. °, -3 |æ| dx |-5

A: GivenI=∫-55-3|x|dxwe know that |x|=xx≥0-xx&lt;0thereforeI=∫-55-3|x|dxI=-3∫-55|x|dxI=-3[∫-50|x|dx +∫0...

Q: 5. Let f(x, y) = x+4 cos y. (a) Evaluate f (0, z/3), f.(0, z /3) and f,(0, x/3). (b) Use the results...

A:  

Q: B. Evaluate the limits of the following: 1. lim Vx2 – 4 x→2+ 2. lim Jx(5 – x) X→5- 4x 3. lim x→4+Vx-...

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Q: Given f(x) 3x Find the following: %3D x – 1 a) f-(x)(2 pts.) b) (fof-!)(0.5) ( 1pt.)

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Q: Sin 10. Im sin ax 12.lim X-0 sinbr X-0

A: We have to find

Q: Homogenous equations (3x² – 2y²)y' = 2xy %3D (Final answer should be in terms of y)

A: Given differential equation is 3x2−2y2y'=2xy.....1 We have to solve the given homogeneous differenti...

Q: Duestion 3 of 18 Find all critical points of the function f(x) = x-" - x-12 (Use symbolic notation a...

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Q: 2x Evaluate / 2r+3 dx 3log(2x+3) + C X - -2 O x – 3log(2x + 3) + C O None 3log(2x+3) х — + C 2

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Q: For f(x) = x2, find dy using the definition, dx dy = lim dx Ду f(x+ Ax) - f(x) lim Ax→0 Ax Ax→0 Ax (...

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Q: Find the four roots of the number 16- as a result of the assumption

A: To find fourth root of 16 by asumption. Let x=164

Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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Q: 4. Evaluate the double integral ry dA where D is enclosed by the curves y = r², y = 3x.

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Q: 1. Use the Chain Rule to find u and ou for w = x²y3 where x = dw at s2 +t2 and y = ds

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Q: (-1, f(t) = Ost 0)

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Q: Using the limit definition, find the derivative of f(x) = tan(ax + b).

A: Consider f(x) = tan (ax + b)

Q: Show that one of the lines givenby 6x² - xy - 12y² = 0 coincides with one of %| the lines givenby 15...

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Q: Behavior of Graphs 3. Use Desmos to create pictures of the following commonly used graphs: y = x y =...

A: Here we have shown all the graph of the equation. 1)  y = x

Q: Use transformations to graph the given function. g(4) 6. 8- 7- 6- 5- 4- -9 -8 -7 -6 -5 4 -3 2 -1 4. ...

A: Given:     gx=15x2 The parent function is fx=x2   y=x25

Q: Evaluate the integral ∫(6x2+1)ln(5x3)dx

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Q: Find a unit vector in the direction in which f(x,y, z) + %3D increases most rapidly at P(1, 2, -2), ...

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Q: Find the orthogonal trajectories of the family of curves ye^4x=C

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Q: Prove that 1-x 1+x -1 cos'x = 2 sin V 2 2cos 2

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Q: If Ax+By+5z=C is an equation for the plane containing the point (0,0,1) and the line x-1=, z=-23, th...

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Q: The size of a certain insect population is given by Pt) = 400e 01 where t is measured in days. At wh...

A: This is a problem of the exponential model of the growth. Based on the given relationship of insect ...

Q: dy and check your result using dx Use the following theorem to find implicit differentiation. If the...

A: To find the dy/dx using the given theorem   

Q: two sheets, ne, elliptic parabolold, or Identify the quadric surface. hyperbolic paraboloid by match...

A: