(5) 0 __sy=x - 6x*+ 8x 2 (Ans. 8 ตารางหน่วย) x

Q: (4)Evaluate the definite integral (a)(1+ si 0 1+ sin x)dx (b) (2t+cost) di (b) f( -x/2 x+ X - dx R/4…

A: Explanation of the answer is as follows

Q: Q1 3 Determine the gradient of the tangent at a point (-2, 1) to a graph of xy² + 3x = x y² - 6

A: gradient of tangent is equal to value of the derivative of the equation at that point.

Q: Describe the graph of the equation. r = − 14i + (1 - t²)j + tk

A: we have given equation

Q: A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude…

A:

Q: What is the value of lim h→0 (1+h)6−1 ? h

A: Let,  This is  indeterminate form.

Q: If the total cost function for producing x lamps is C(x) = 960 +31x + 0.6x² dollars, producing how…

A:

Q: dx x°+2x (Ans. In 2 X x+2 +C)

A:

Q: The fox population in a certain region has a continuous growth rate of 8 percent per year. It is…

A:

Q: If |A| = 9 and |B| = 7, what is |A U B|+|An B|?

A: =9 ,=7 to find |+

Q: -4 3. y = (²-²)sec¯¹ (4 + x²³)

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: evaluate the integral. Your answer should not contain f, which is a differentiable function with the…

A:

Q: Find T(t) and N(t) at the given point. ㅠ r(t) = 4 cos(t)i +4sin(t)j; t = 73 T(₁) N(₁7) = 3. 13

A: The given vector Here

Q: x=t and y=t-1 for -2≤t≤2 Part: 0 / 2 Part 1 of 2 (a) Use the parametric equations to compute x and y…

A:

Q: Find 2. by Implicit Differentiation method dx k+5 = 8

A: Use implicit differentiation method find dy/dx.If

Q: Em f(x) is equivalent to g(0) when f= x O True and g(x)=x O False

A:

Q: Find a Cartesian equation for the curve represented by the given Polar equation. (a) r = -2 (b) T =…

A: We have polar form equationWe have to convert it in cartesian form

Q: Given a = 4i - 7k in R³, determine a) a in component form b) la (exact value)

A: given vector

Q: Find the directional derivative of f(x, y) = √√/7x+ 5y at the point (4,0) in the direction -2п 3…

A: We have to find the directional derivative

Q: Evaluate the limit along the stated paths, or type "DNE" if the limit Does Not Exist: xy + y³ lim…

A:

Q: Find the derivative of: -7√x- 6 x7 Type your answer without fractional or negative er

A: The given equation

Q: Use the Trapezoidal Rule to approximate (2x² + 1) dx using n = 4. Round your answer to the nearest…

A: We can find the integral using trapezoidal rule and it's exact value and then compare them.

Q: 2 x+3x³-5x²-4x+17 {+85-₂8 + {² dx (Ans. +2x-3-In/x²+2x-3+C)

A:

Q: Solve AABC subject to the given conditions. A=9.6°, C=98.5°, b=62

A: we have given

Q: A poster of area 19440 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on…

A:

Q: Use l'Hôpital's Rule to evaluate the limit. x² - 8x+15 x-3 lim x-3 OA. 6- OB. 14 OC. -2 OD. -5

A: Limx-3(x2-8x+15)/(x-3) Find the limit.

Q: sőt s to x6 sdxdy (x²+y²)z

A:

Q: 1. Is the series convergent En>2 n(Inn)?

A:

Q: Find a unit vector in the direction of s=-3.91-5.2j. Express your answer as a decimal in terms of i…

A:

Q: What is the square root of 2512 ? Give the answer in the same form as the number shown here.

A: Consider the number   2512

Q: Solve the inequality. Write the solution set in inter 2 4x + 12x-9<0 Choose the correct solution…

A:

Q: lim √x+2 does not exist when OC = 4 O the limit exists for any c O c = 0 C = 2

A: We have f(x)= (X+2)1/3      We have to find value of 'c' for which limit of f(x) exist as x…

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dy dt x² + 2y²…

A:

Q: (1) [(x²-4)³(2x) dx ; u=x²-4

A: given integration

Q: Use the formula K(t) k(t): ||r'(t) x r" (t)|| ||r' (t) ||³ r(t) = 7 cos(4t)i + 7 sin(4t)j + 5tk = =…

A:

Q: If ƒ(x) = f'(x) = f'(2) = √x-6 √√x +6' " find:

A:

Q: While on a camping trip, a camper hung their food bag using two ropes between two trees. One rope…

A:

Q: 1–52 1+5x Let f(x) = Then f'(2) is and f'(2) is

A: Let .To find  and .

Q: what, if anything, does the comparison tell us about the convergence of the integral? Jo √x dx,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 2. Evaluate [ F C F = (xz, 0, yz) and the path C is the line segment from point (-1,2,0) to (3,0,1)…

A: Given that, Now,

Q: Find the second order partial derivatives of the following function  f(x, y) = 2x^2y+ 2 + 3e^x sin…

A: The given function is:

Q: 1²+y³ i) lim(x,y) (0,0) z²+y²+1

A: We have to find limit of (x2+y3)/(x2+y2+1)as (x,y) approaches (0,0)

Q: Q1 Find the radius and the interval of convergence of (3x - 2)" n the power series > n=1 work. -.…

A: The given series is summation of(3x-2) n/n , n from 1 to infinity.

Q: 3 In the standard equation for a conic section Ax² + Bxy + Cy² + Dx + Ey + F= 0, if B2-4AC > 0, the…

A:

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A: The given function is f(x)=7xFind the maclaurin series and radius of convergence.

Q: Consider the vectors u = 2i + 3j − k and v = 5i − 4j + 2k. Find the following: i) Find the sum u + v…

A: The given vectors are u=2i+3j-k, v=5i-4j+2kAs per the rules, we are supposed to answer the first…

Q: Р Find the directional derivative of the function fo the vector (3,-3).

A:

Q: State the domain and range of the function f(x) = 13+ log7(x) Answer: domain= range = ↳ ✓

A:

Q: Find the foci of the following hyperbola: + 1)²_ @x_1² = 1 (v (x-1)² 25 O (-1+√34,-1); (-1 – √34,…

A: The given equation is; (y+1)2/9 - (x-1) 2/25 =1Find foci.

Q: Find the point on the line -3x + 3y + 1 = 0 which is closest to the point (−1, 3).

A:

Q: Let -3x³+3y³ + 2x³ + xyz - 673 = 0. Oz дх Oz Use partial derivatives to calculate and at the point…

A: The equation is given by:-We need to find the at point