The gradient of f(x, y) = e²z sin(1- y) at (x, y) = (1, -1) is defined as followed: V f(x, y) = (fz(1, − 1), fy(1, − 1)). - Then fz(1, -1) = fy(1, -1) = Calculator Check Answer

Q: d (tan² (2x³)). dx (a) 202¹ tan (2x5) sec² (2x5) (b) 20x¹ tan (25) 16. Calculate (c) 2 tan (2x5) (d)…

A:

Q: y sin(x) = x sin(y²)

A: y sin(x2) = x sin(y2)

Q: Let p be a prime. Prove that ((p-1)!+1) = 0 (mod p).

A: Let p be a prime . then

Q: find derivative of f(x) = x (x²+3x) O x² +3x O x² +6x O 3x² +6 x O none of these answers

A:

Q: Find the values of a and b for which g(x) is continuous for all x. -5 if x < -1 ax+b if -1 < x < 1…

A:

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x-7…

A:

Q: Find the dimensions of the box with the maximum volume

A:

Q: Please quickly The equation (Picture 1) is defined as the set of points equidistant from the point…

A:

Q: A box of volume 216 m³ with a square bottom and no top is made of two different materials. The cost…

A: Let  The length of the bottom side = x  height = y    volume = 216  x·x·y=216     y=216x2

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: fx,y=ln5+x2y2

Q: Find the first partial derivatives with respect to x, y, and z. w = x7yz2 + xy − 4yz

A:

Q: If f(x) = Σ n=0 n=0 2n ∞ 2n an and g(x) = Σ (1)" 20 am, find the power series of (f(x) + g(x)). n!…

A:

Q: s) Let f(x) = ³√x. (a) Use linear approximation at x = 1 to approximate f(0.6)= 30.6. The Linear…

A:

Q: Sketch the graph of y = sin(x) in the interval -720° < x < 720°.

A: To plot the graph of sin(x) over [-720o,720o].

Q: What is the sum of the first six terms of the geometric series 2-4+8-... ? α₁ (1-²¹) 1-r Sn = O S6…

A:

Q: 11) (a) Find the general anti-derivative, F(x), given f(x) = = 3x²+5x-8 1+x²

A: To find the general anti-derivative, Fx, given fx=3x2+5x-8x2-11+x2.   Note: Since the student has…

Q: [x+y+z=0 Solve the system of linear equation 3x+ 5y + 4z = 5 using the following four methods:…

A: given system of equation can be expressed can be represented in matrix form as AX = B where…

Q: Let {an} be the recursively-defined sequence where 7n²+ n-3 a₁ = 4 and an+1 = Determine whether the…

A:

Q: x-f(x) 2x + 3 Find k'(-2), given that Let k(x)= Provide your answer below: K'(-2)= f(-2) = -3,…

A:

Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A:

Q: 2. Consider f(x) = ax³ + x + 1, where a is a real-valued parameter. Find all possible values of a…

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: f(x) = x² ex find derivative

A: Differentiate the given function  f(x)= x2ex

Q: A polar equation is given. 10 3-2 cos(8) FM (a) Find the eccentricity. Use this information to…

A:

Q: Consider the following vector field. F(x, y, z) = (3ex sin(y), 5ex sin(z), 7e² sin(x)) (a) Find the…

A:

Q: What is the common ratio of the geometric sequence? tn 40 35 30 25 20 15 10 5 Or=2 Or=1/12 O r = -20…

A: Terms of Geometric sequence,

Q: Evaluate the limit. [A] 5 615 [B] = [C] O lim x-0 [D] 1 sin (2x)cos (3x) 5x 25 [E] }

A:

Q: Find the points at which the following function is discontinuous. 8x + 1 f(x) = 5x-8 6x²6 Select the…

A: The given function is f(x)=8x+1if x≤-35x-8if  -3&lt;x≤36x2-6if x&gt;3 Since polynomial functions are…

Q: 3. Find g'(x) = I 1 9x5 + 2 3x4 1 X

A:

Q: Find the mass of a lamina bounded by y = 5√x, x = 4, and y = 0 with the density function o(x, y) = x…

A:

Q: B) Find an expression (f₂) for the rate of change of output with respect to the number of skilled…

A:

Q: End a f4 4x cos (11 - 5x²) dx. Simplify your answer. Answer:

A: ∫ 4x· cos11-5x2dx

Q: 4 x²-3x³ + 2x² +2x²+x+1 +x+1 3 x² + 2x dx

A:

Q: √x √x + √√y = 1

A:

Q: Using implicit differentiation, find Provide your answer below: dy dx dy dx √xy = -5 + xy FEEDBACK

A:

Q: 5. Find the arc length of the spiral r=0 from 0=0 to 0=27.

A: Arc length for a function of the form r=rθ from θ=θ1 to θ=θ2 is given by ∫θ1θ2rθ2+r'θ2  dθ.

Q: Find the limit L (if it exists). If it does not exist, explain why. (If an answer does not exist,…

A: We find common terms then cancel it out so we find limits

Q: Find dx dt dx dt at x = -2 if y=-2x² - 4 and dy dt = -2.

A:

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x…

A: The given function fx=xcos5x. We have to find the Maclaurin series for the function.

Q: Graph: y=2cos2x+4

A: To graph the following function. y=2 cos2x+4

Q: 3 F(x) = x² ³√√ 1-2x²-7X Find The F(X)

A: F(x)=x3(1-2x2-7x)1/3 We have to find F'(x)

Q: Anthony rides a train along a straight north-south track. His position at time ₺ in hour is s(t) =…

A: Let position function denoted by s( t ) Let velocity function denotes by v( t ) Average velocity…

Q: -) A closed box with square base is to be built to house an ant colony. The bottom of the box and…

A: Given that A closed box is to be built to house an ant  colony. Now,

Q: 9 Consider the function f(x) = 3x³ + 6x6 – 7x³ – 5. - An antiderivative of f(x) is F(x) = Ax" + Bx"…

A:

Q: 13. dy dx dy = dx ex cos y e2y cos x -e-* sin y + 2e²y sin x 2x + 3y -

A:

Q: Ap 0 -2 On what intervals is f'(x) > 0? On what intervals is f"(x) < 0? 2 X

A: The given graph of function f(x) is:

Q: 3. Evaluate the path integral fo(y + tan(x)) dx + (2x − 4 ln(y²)) dy, where C is the ellipse 16x² +…

A:

Q: ,2/3 = 4 x2/3 + y2/3 (-3√3, 1) (astroid) ул 0 8 X

A:

Q: (a) Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.31). L(x) = In…

A: Linear approximation at x=a of function fxLx≈fa+f'ax-a

Q: Find the area inside the cardioid r=1+cos but outside the circle r=1.

A: Note:-  since you asked question 4 to solve ,so we solve question 4 for you  Given equations:-…

Q: ). Find the total area of the shaded region shown to the right given by the curve y = 4( sin x)√1 +…

A: